Showing papers on "Robust control published in 2020"
TL;DR: This paper proposes a multi-stage procedure that estimates a model from a few experimental trials, estimates the error in that model with respect to the truth, and then designs a controller using both the model and uncertainty estimate, and provides end-to-end bounds on the relative error in control cost.
Abstract: This paper addresses the optimal control problem known as the linear quadratic regulator in the case when the dynamics are unknown. We propose a multistage procedure, called Coarse-ID control, that estimates a model from a few experimental trials, estimates the error in that model with respect to the truth, and then designs a controller using both the model and uncertainty estimate. Our technique uses contemporary tools from random matrix theory to bound the error in the estimation procedure. We also employ a recently developed approach to control synthesis called System Level Synthesis that enables robust control design by solving a quasi-convex optimization problem. We provide end-to-end bounds on the relative error in control cost that are optimal in the number of parameters and that highlight salient properties of the system to be controlled such as closed-loop sensitivity and optimal control magnitude. We show experimentally that the Coarse-ID approach enables efficient computation of a stabilizing controller in regimes where simple control schemes that do not take the model uncertainty into account fail to stabilize the true system.
489 citations
TL;DR: In this paper, the authors derive a parametrization of linear feedback systems that paves the way to solve important control problems using data-dependent linear matrix inequalities only, which is remarkable in that no explicit system's matrices identification is required.
Abstract: In a paper by Willems et al., it was shown that persistently exciting data can be used to represent the input-output behavior of a linear system. Based on this fundamental result, we derive a parametrization of linear feedback systems that paves the way to solve important control problems using data-dependent linear matrix inequalities only. The result is remarkable in that no explicit system's matrices identification is required. The examples of control problems we solve include the state and output feedback stabilization, and the linear quadratic regulation problem. We also discuss robustness to noise-corrupted measurements and show how the approach can be used to stabilize unstable equilibria of nonlinear systems.
314 citations
TL;DR: The Disturbance Observer (DOB) has been one of the most widely used robust control tools since it was proposed by Ohnishi in 1983 as mentioned in this paper, and it has been widely used in robust control applications.
Abstract: Disturbance observer (DOB) has been one of the most widely used robust control tools since it was proposed by Ohnishi in 1983. This paper introduces the origins of DOB and presents a survey of the major results on DOB-based robust control in the last 35 years. Furthermore, it explains DOB's analysis and synthesis techniques for linear and nonlinear systems by using a unified framework. In final section, this paper presents concluding remarks on DOB-based robust control and its engineering applications.
207 citations
TL;DR: This article focuses on the containment control problem for nonlinear multiagent systems (MASs) with unknown disturbance and prescribed performance in the presence of dead-zone output, and a new distributed containment control scheme is developed by utilizing the adaptive compensation technique without assumption of the boundary value of unknown disturbance.
Abstract: This article focuses on the containment control problem for nonlinear multiagent systems (MASs) with unknown disturbance and prescribed performance in the presence of dead-zone output. The fuzzy-logic systems (FLSs) are used to approximate the unknown nonlinear function, and a nonlinear disturbance observer is used to estimate unknown external disturbances. Meanwhile, a new distributed containment control scheme is developed by utilizing the adaptive compensation technique without assumption of the boundary value of unknown disturbance. Furthermore, a Nussbaum function is utilized to cope with the unknown control coefficient, which is caused by the nonlinearity in the output mechanism. Moreover, a second-order tracking differentiator (TD) is introduced to avoid the repeated differentiation of the virtual controller. The outputs of the followers converge to the convex hull spanned by the multiple dynamic leaders. It is shown that all the signals are semiglobally uniformly ultimately bounded (SGUUB), and the local neighborhood containment errors can converge into the prescribed boundary. Finally, the effectiveness of the approach proposed in this article is illustrated by simulation results.
143 citations
13 Jan 2020
TL;DR: The ability of policies learned within this simulator to generalize to and navigate in previously unseen real-world roads, without access to any human control labels during training is demonstrated.
Abstract: In this work, we present a data-driven simulation and training engine capable of learning end-to-end autonomous vehicle control policies using only sparse rewards. By leveraging real, human-collected trajectories through an environment, we render novel training data that allows virtual agents to drive along a continuum of new local trajectories consistent with the road appearance and semantics, each with a different view of the scene. We demonstrate the ability of policies learned within our simulator to generalize to and navigate in previously unseen real-world roads, without access to any human control labels during training. Our results validate the learned policy onboard a full-scale autonomous vehicle, including in previously un-encountered scenarios, such as new roads and novel, complex, near-crash situations. Our methods are scalable, leverage reinforcement learning, and apply broadly to situations requiring effective perception and robust operation in the physical world.
136 citations
TL;DR: An radial basis function (RBF) neural network based adaptive robust control design is proposed for nonlinear bilateral teleoperation manipulators to cope with the main issues including the communication time delay, various nonlinearities, and uncertainties.
Abstract: The bilateral teleoperation system has raised expansive concern as its excellent behaviors in executing the tasks in the remote, unstructured, and dangerous areas via the cooperative operation systems. In this article, an radial basis function (RBF) neural network based adaptive robust control design is proposed for nonlinear bilateral teleoperation manipulators to cope with the main issues including the communication time delay, various nonlinearities, and uncertainties. Specifically, the slave environmental dynamics is modeled by a general RBF neural network, and its parameters are estimated and then transmitted for the environmental torque reconstruction in the master side. Since the parameters of the neural network (which are nonpower signals) are transmitted instead of the traditional environmental torque in the communication channel, the previous existing passivity problem under time delay is avoided. In both of master and slave sides, the trajectory creators are applied to generate the desired trajectories, and the RBF-neural-network-based adaptive robust controllers are designed subsequently to handle the nonlinearities and uncertainties. Theoretically, the proposed control algorithm can guarantee the global stability of bilateral teleoperation manipulators under time delay, and the good transparency performance with both position tracking and force feedback is also achieved simultaneously. The real platform comparative experiments are carried out, and the results show the good position tracking to execute precise operation and the good force feedback to detect the sudden disturbance in the environment dynamics.
132 citations
TL;DR: The proposed control approach significantly improves the controller’s robustness in the face of uncertain signal timing, without requiring to know the distribution of the random variable a priori.
Abstract: This article focuses on the speed planning problem for connected and automated vehicles (CAVs) communicating to traffic lights. The uncertainty of traffic signal timing for signalized intersections on the road is considered. The eco-driving problem is formulated as a data-driven chance-constrained robust optimization problem. Effective red-light duration (ERD) is defined as a random variable, and describes the feasible passing time through the signalized intersections. Usually, the true probability distribution for ERD is unknown. Consequently, a data-driven approach is adopted to formulate chance constraints based on empirical sample data. This incorporates robustness into the eco-driving control problem with respect to uncertain signal timing. Dynamic programming (DP) is employed to solve the optimization problem. The simulation results demonstrate that the proposed method can generate optimal speed reference trajectories with 40% less vehicle fuel consumption, while maintaining the arrival time at a similar level compared to a modified intelligent driver model (IDM). The proposed control approach significantly improves the controller’s robustness in the face of uncertain signal timing, without requiring to know the distribution of the random variable a priori .
110 citations
TL;DR: A deep reinforcement learning-based robust control strategy for quadrotor helicopters which introduces an integral compensator to the actor-critic structure and shows that the online learning could significantly improve the control performance.
Abstract: In this paper, a deep reinforcement learning-based robust control strategy for quadrotor helicopters is proposed. The quadrotor is controlled by a learned neural network which directly maps the system states to control commands in an end-to-end style. The learning algorithm is developed based on the deterministic policy gradient algorithm. By introducing an integral compensator to the actor-critic structure, the tracking accuracy and robustness have been greatly enhanced. Moreover, a two-phase learning protocol which includes both offline and online learning phase is proposed for practical implementation. An offline policy is first learned based on a simplified quadrotor model. Then, the policy is online optimized in actual flight. The proposed approach is evaluated in the flight simulator. The results demonstrate that the offline learned policy is highly robust to model errors and external disturbances. It also shows that the online learning could significantly improve the control performance.
109 citations
01 Jul 2020
TL;DR: This work considers the problem of designing robust state-feedback controllers for discrete-time linear time-invariant systems, based directly on measured data, and shows how the proposed framework can be extended to take partial model knowledge into account.
Abstract: We consider the problem of designing robust state-feedback controllers for discrete-time linear time-invariant systems, based directly on measured data. The proposed design procedures require no model knowledge, but only a single open-loop data trajectory, which may be affected by noise. First, a data-driven characterization of the uncertain class of closed-loop matrices under state-feedback is derived. By considering this parametrization in the robust control framework, we design data-driven state-feedback gains with guarantees on stability and performance, containing, e.g., the ℋ
∞
-control problem as a special case. Further, we show how the proposed framework can be extended to take partial model knowledge into account. The validity of the proposed approach is illustrated via a numerical example.
106 citations
TL;DR: Batteries of electric vehicles are employed to assist power plants to swiftly arrest oscillations in the system frequency following load demands and a novel optimal cascade fuzzy-fractional order integral derivative with filter (CF-FOIDF) controller is utilised for 2-area thermal and hydrothermal PSs.
Abstract: Load frequency control in modern-complex-uncertain power systems (PSs) assumes significance due to their challenging nature of the operation and hence utilisation of robust controllers is indispensable. In the industry, conventional single-loop controllers may not offer robust behaviour under changed operating conditions. Alternatively, two-loop cascade fuzzy structured controllers can show significant robust performance in dynamic conditions and best suited in systems having non-linearities. Hence, a novel optimal cascade fuzzy-fractional order integral derivative with filter (CF-FOIDF) controller is utilised for 2-area thermal and hydrothermal PSs considering various physical constraints from a practical point of view. As physical constraints mandate an energy storage system, hence in this study, batteries of electric vehicles (EVs) are employed to assist power plants to swiftly arrest oscillations in the system frequency following load demands. A combined model of EV fleets is incorporated in the control areas of PSs. Numerous simulations are conducted to authenticate the robustness and excellence of EVs and the suggested control strategy over existing methods.
97 citations
TL;DR: It is proved that the proposed approach guarantees output tracking with prescribed accuracy and constraint satisfactions simultaneously, even if actuator faults occur, and a new-type error boundary is introduced to the control design.
TL;DR: A new robust controller is developed for robot manipulator based on an integrating between a novel self-tuning fuzzy proportional-integral-derivative (PID)-nonsingular fast terminal sliding mode control (STF-PID-NFTSM) and a time delay estimation (TDE).
Abstract: In this work, a new robust controller is developed for robot manipulator based on an integrating between a novel self-tuning fuzzy proportional-integral-derivative (PID)-nonsingular fast terminal sliding mode control (STF-PID-NFTSM) and a time delay estimation (TDE). A sliding surface based on the PID-NFTSM is designed for robot manipulators to get multiple excited features such as faster transient response with finite time convergence, lower error at steady-state and chattering elimination. However, the system characteristics are hugely affected by the selection of the PID gains of the controller. In addition, the design of the controller requires an exact dynamics model of the robot manipulators. In order to obtain effective gains for the PID sliding surface, a fuzzy logic system is employed and in order to get an estimation of the unknown dynamics model, a TDE algorithm is developed. The innovative features of the proposed approach, i.e., STF-PID-NFTSM, is verified when comparing with other up-to-date advanced control techniques on a PUMA560 robot.
TL;DR: This article studies the robust trajectory tracking control problem of a quadrotor unmanned aerial vehicle (UAV) and proposes a novel backstepping sliding-mode control scheme for position subsystem that is robust to the external disturbances and model uncertainties.
Abstract: This article studies the robust trajectory tracking control problem of a quadrotor unmanned aerial vehicle (UAV). In order to guarantee the desired trajectory tracking performance in the presence of external disturbances and model uncertainties, the design process of the quadrotor UAV controller is divided into two steps. First, by decomposing the attitude dynamic system into two serial-connected subsystems, a cascade active disturbance rejection control scheme is applied to the attitude subsystem. Second, by introducing an additional high-gain design parameter, a novel backstepping sliding-mode control scheme for position subsystem is constructed. Moreover, the Lyapunov stability analysis is provided to show that the trajectory tracking error can converge to an arbitrarily small residual set. Numerical results illustrate the effectiveness of the designed control method and its robustness to the external disturbances and model uncertainties. Finally, the proposed method is implemented on a quadrotor UAV to demonstrate its feasibility in practical application.
TL;DR: In this paper, a robust iterative learning control (ILC) algorithm is derived based on iteratively solving this problem and a numerical simulation case study is conducted to compare the performance of this algorithm with other control algorithms while performing a given point-to-point tracking task.
Abstract: Iterative learning control (ILC) is a high-performance technique for repeated control tasks with design postulates on a fixed reference profile and identical initial conditions. However, the tracking performance is only critical at few points in point-to-point tasks, and their initial conditions are usually trial-varying within a certain range in practice, which essentially degrades the performance of conventional ILC algorithms. Therefore, this study reformulates the ILC problem setup for point-to-point tasks and considers the effort of trial-varying initial conditions in algorithm design. To reduce the tracking error, it proposes a worst-case norm-optimal problem and reformulates it into a convex optimisation problem using the Lagrange dual approach. In this sense, a robust ILC algorithm is derived based on iteratively solving this problem. The study also shows that the proposed robust ILC is equivalent to conventional norm-optimal ILC with trial-varying parameters. A numerical simulation case study is conducted to compare the performance of this algorithm with that of other control algorithms while performing a given point-to-point tracking task. The results reveal its efficiency for the specific task and robustness against trial-varying initial conditions.
TL;DR: This work proposes a model-free robust control for cable-driven manipulators with disturbance using a new NFTSM surface utilizing a new continuous TSM-type switch element to achieve accurate, singularity-free and fast dynamical control performance.
Abstract: This work proposes a model-free robust control for cable-driven manipulators with disturbance. To achieve accurate, singularity-free and fast dynamical control performance, we design a new NFTSM surface utilizing a new continuous TSM-type switch element. By replacing the integral power with fractional one for the error dynamics, the designed TSM-type switch element can effectively enhance the dynamical performance of the NFTSM surface. Time-delay estimation (TDE) technique is applied to cancel out complicated nonlinear dynamics guaranteeing an excellent model-free scheme. Thanks to the designed NFTSM surface, adopted reaching law and TDE, our control can provide good comprehensive control performance effectively. Stability and comparisons of control precision and convergence speed have been theoretically analyzed. Finally, comparative experiments were conducted to prove the superiorities of our control.
TL;DR: This article solves the safe trajectory tracking control problem of robot manipulators with actuator faults, uncertain dynamics, and external disturbance by designing an adaptive control law designed by using the joint position, the estimated velocity, and the reconstructed knowledge of velocity measurement uncertainty.
Abstract: This article solves the safe trajectory tracking control problem of robot manipulators with actuator faults, uncertain dynamics, and external disturbance. Another key issue met in practical robot engineering, i.e., joint velocity measurement uncertainty is also investigated. A robust control framework is presented. In this approach, a novel reconstruction law is preliminarily developed to estimate velocity measurement uncertainty, while the estimation error is finite-time stable. An adaptive control law is, then, designed by using the joint position, the estimated velocity, and the reconstructed knowledge of velocity measurement uncertainty. The key advantage of this methodology is that actual joint velocity and any prior knowledge of actuator faults are not required. The effectiveness of this proposed scheme is experimentally validated on a real robot arm.
TL;DR: An improved differential evolution algorithm, referred to as multiple-samples and mixed-strategy DE (msMS_DE), is proposed to search robust fields for various quantum control problems to demonstrate the excellent performance of the improved machine learning algorithm for these two classes of quantum robust control problems.
Abstract: Robust control design for quantum systems has been recognized as a key task in quantum information technology, molecular chemistry, and atomic physics. In this paper, an improved differential evolution algorithm, referred to as multiple-samples and mixed-strategy DE ( msMS _DE), is proposed to search robust fields for various quantum control problems. In msMS _DE, multiple samples are used for fitness evaluation and a mixed strategy is employed for the mutation operation. In particular, the msMS _DE algorithm is applied to the control problems of: 1) open inhomogeneous quantum ensembles and 2) the consensus goal of a quantum network with uncertainties. Numerical results are presented to demonstrate the excellent performance of the improved machine learning algorithm for these two classes of quantum robust control problems. Furthermore, msMS _DE is experimentally implemented on femtosecond (fs) laser control applications to optimize two-photon absorption and control fragmentation of the molecule CH2BrI. The experimental results demonstrate the excellent performance of msMS _DE in searching for effective fs laser pulses for various tasks.
TL;DR: A two-layer Model Predictive Control (MPC) is developed so that more efficient control signals are provided to improve the response of BESSs to make larger contribution to the LFC.
Abstract: This paper proposes a robust control scheme to involve the distributed Battery Energy Storage Systems (BESSs) in Load Frequency Control (LFC) through BESS aggregators with sparse communication networks. In order to cope with the uncertainties associated with system operation, a two-layer Model Predictive Control (MPC) is developed so that more efficient control signals are provided to improve the response of BESSs to make larger contribution to the LFC. The outer layer in the proposed structure produces the command signal for the aggregator based on signals which are produced by the inner layer as well as the signal provided from the actual system. These command signals are provided so as to achieve the least value of error in Area Control Error (ACE) with a minimum control effort taking a variety of operational and physical constraints into consideration. Optimization procedures are also carried out to compute the optimal value of weighting coefficients contained in the objective functions. The capability of controller to cope with uncertainties is compared with a conventional single-layer MPC. In addition, the delay caused by propagation channels in delivering control signals to BESSs is modeled, and its impact on the performance of frequency regulation is evaluated. An intelligent fuzzy coordination control is then developed to coordinate the BESS aggregator and conventional power plants to avoid extra power injection/withdrawal by the conventional power plants in case of long delays. Case studies are conducted to illustrate the effectiveness of the proposed structure in controlling distributed BESSs with diverse energy capacities, rated powers, charging/discharging coefficients and time constants; and State of Charges (SoCs).
TL;DR: A robust fractional-order sliding-mode control of a fully active battery/supercapacitor hybrid energy storage system used in electric vehicles (EVs) is designed and a hardware-in-the-loop (HIL) test is undertaken to validate the effectiveness of the proposed control scheme.
TL;DR: Some sufficient conditions for the exponential stability of the cyber-physical delayed-switching system are developed, which guarantees the robustness of the proposed strategy against the communication delays and dynamically changing interaction topologies.
Abstract: In this paper, a robust neighbor-based distributed cooperative control strategy is proposed for dc cyber-physical microgrids, considering communication delays and slow switching topologies. The proposed robust control strategy can synchronize the voltages of a dc microgrid to the desired value while achieving the optimal load sharing for minimizing distributed energy resources’ (DERs) generation cost to achieve their economic operation at the same layer via a sparse communication network considering communication delays and slow switching topologies synchronously. The continuous interaction of physical–electrical and cyber networks generally exacerbates the occurrence of communication delays. Moreover, the arbitrary switching topologies could destroy the system’s transient characteristics at the switching time instants. To further quantify these impacts on the system stability, the communication delay and average switching dwell-time-dependent control conditions for the proposed control strategy are proved based on the Lyapunov–Krasovskii theory. Some sufficient conditions for the exponential stability of the cyber-physical delayed-switching system are developed, which guarantees the robustness of the proposed strategy against the communication delays and dynamically changing interaction topologies. The proposed control protocols are shown to be fully distributed and implemented through a sparse communication network. Finally, several cases on a modified IEEE 34-bus test network are investigated which demonstrate the effectiveness and performance of the results.
TL;DR: The proposed robust optimal control algorithm tunes the parameters of critic-only neural network by event-triggering condition and runs in a plug-n-play framework without system functions, where fewer transmissions and less computation are required as all the measurements received simultaneously.
Abstract: In this paper, a novel event-sampled robust optimal controller is proposed for a class of continuous-time constrained-input nonlinear systems with unknown dynamics. In order to solve the robust optimal control problem, an online data-driven identifier is established to construct the system dynamics, and an event-sampled critic-only adaptive dynamic programming method is developed to replace the conventional time-driven actor–critic structure. The designed online identification method runs during the solving process and is not applied as a priori part for the solutions, which simplifies the architecture and reduces computational load. The proposed robust optimal control algorithm tunes the parameters of critic-only neural network (NN) by event-triggering condition and runs in a plug-n-play framework without system functions, where fewer transmissions and less computation are required as all the measurements received simultaneously. Based on the novel design, the stability of system and the convergence of critic NN are demonstrated by Lyapunov theory, where the state is asymptotically stable and weight error is guaranteed to be uniformly ultimately bounded. Finally, the applications in a basic nonlinear system and the complex rotational–translational actuator problem demonstrate the effectiveness of the proposed method.
TL;DR: A new sliding surface is first proposed and a robust control is developed for ensuring global approximate fixed-time convergence of tracking errors and it is proven that the position tracking errors globally converge to an arbitrary small set within a uniformly bounded time and then go to zero exponentially.
TL;DR: Benefiting from the proposed nonlinear adaptive law, suppression of chattering issue and enhanced control performance have been obtained simultaneously.
Abstract: In this article, we propose a novel adaptive time-delay control (ATDC) for accurate trajectory tracking of cable-driven robots. The designed ATDC utilizes time-delay estimation (TDE) to estimate the lumped dynamics of the system and provides an attractive model-free structure. Then, a robust control is designed for ATDC with fractional-order nonsingular terminal sliding mode (FONTSM) dynamics. Afterward, a novel nonlinear adaptive law is proposed for the control gains to improve the control performance. Thanks to TDE and FONTSM dynamics, the proposed ATDC is model free and highly accurate. Benefiting from the proposed nonlinear adaptive law, suppression of chattering issue and enhanced control performance have been obtained simultaneously. Stability is analyzed based on the Lyapunov approach. Then, practical experiments have been performed to illustrate the advantages of the proposed ATDC.
TL;DR: Different methods of primary control for current and voltage regulation, secondary control for error-correction in voltage and current, power sharing in a microgrid and microgrid clusters and tertiary control for power and energy management with a primary focus on minimal power loss and operational cost in a DC microgrid system are reviewed in-depth.
Abstract: This work presents an extensive review of hierarchical control strategies that provide effective and robust control for a DC microgrid. DC microgrid is an efficient, scalable and reliable solution for electrification in remote areas and needs a reliable control scheme such as hierarchical control. The hierarchical control strategy is divided into three layers namely primary, secondary and tertiary based on their functionality. In this study, different methods of primary control for current and voltage regulation, secondary control for error-correction in voltage and current, power sharing in a microgrid and microgrid clusters and tertiary control for power and energy management with a primary focus on minimal power loss and operational cost in a DC microgrid system are reviewed in-depth. Along with this, the advantages and limitations of various control structures like centralised, decentralised, distributed are discussed in this study. After a comparative study of all control strategies, the optimum control schemes from the author's point of view are also presented.
TL;DR: To achieve precision motion control, an adaptive robust control with a backstepping design is proposed for an electrohydraulic system, where the cylinder actuator is direct-driven by a servomotor pump.
Abstract: Pump control hydraulic systems can achieve high efficiency by the advantages of no throttling loss and high power-to-volume ratio. However, low tracking accuracy and slow frequency response are main drawbacks for the applications of pump control hydraulic systems, because of the existing high-order dynamics, uncertainties, and highly nonlinear dynamics. Recently, the advent of servomotor-pump direct-drive electrohydraulic systems shows a good prospect for this issue, and the design of the control algorithm is the key to achieve high motion accuracy. In this article, to achieve precision motion control, an adaptive robust control with a backstepping design is proposed for an electrohydraulic system, where the cylinder actuator is direct-driven by a servomotor pump. Considering the high-order dynamics and nonlinearities of hydraulic systems, the controller is processed in two steps: position tracking step and pressure step. Besides, the pump flow deviation under low speed is another important limitation for good control performance. Thus, a nonlinear pump flow rate mapping is proposed by practical fitting and used into the controller design by the proper nonlinearity compensation of the desired pump flow. Comparative experiment results show that the proposed control strategy achieves high motion control performances in spite of the nonlinearities and uncertainties.
TL;DR: In this article, the robust fault detection filter design problem for a class of discrete-time conic-type non-linear Markov jump systems with jump fault signals was investigated, and sufficient conditions for the existence of the designed filter were presented in terms of linear matrix inequalities.
Abstract: This study investigates the robust fault detection filter design problem for a class of discrete-time conic-type non-linear Markov jump systems with jump fault signals. The conic-type non-linearities satisfy a restrictive condition that lies in an n-dimensional hyper-sphere with an uncertain centre. A crucial idea is to formulate the robust fault detection filter design problem of non-linear Markov jump systems as H ∞ filtering problem. The authors aim to design a fault detection filter such that the augmented Markov jump systems with conic-type non-linearities are stochastically stable and satisfy the given H ∞ performance against the external disturbances. By means of the appropriate mode-dependent Lyapunov functional method, sufficient conditions for the existence of the designed fault detection filter are presented in terms of linear matrix inequalities. Finally, a practical circuit model example is employed to demonstrate the availability of the main results.
TL;DR: This survey discusses well-known theoretical and engineering problems in which hidden oscillations (their absence or presence and location) play an important role.
Abstract: The development of the theory of absolute stability, the theory of bifurcations, the theory of chaos, theory of robust control, and new computing technologies has made it possible to take a fresh look at a number of well-known theoretical and practical problems in the analysis of multidimensional control systems, which led to the emergence of the theory of hidden oscillations, which represents the genesis of the modern era of Andronov’s theory of oscillations. The theory of hidden oscillations is based on a new classification of oscillations as self-excited or hidden. While the self-excitation of oscillations can be effectively investigated analytically and numerically, revealing a hidden oscillation requires the development of special analytical and numerical methods and also it is necessary to determine the exact boundaries of global stability, to analyze and reduce the gap between the necessary and sufficient conditions for global stability, and distinguish classes of control systems for which these conditions coincide. This survey discusses well-known theoretical and engineering problems in which hidden oscillations (their absence or presence and location) play an important role.
Posted Content•
11 Sep 2020
TL;DR: The approach leads to linear matrix inequality (LMI) based feasibility criteria which guarantee stability, $\mathcal{H}_2$-performance, or quadratic performance robustly for all closed-loop systems consistent with the prior knowledge and the available data.
Abstract: We present a framework for systematically combining data of an unknown linear time-invariant system with prior knowledge on the system matrices or on the uncertainty for robust controller design. Our approach leads to linear matrix inequality (LMI) based feasibility criteria which guarantee stability and performance robustly for all closed-loop systems consistent with the prior knowledge and the available data. The design procedures rely on a simple data-dependent uncertainty bound which can be employed for controller design using dualization arguments and S-procedure-based LMI relaxations. While most parts of the paper focus on input-state measurements, we also provide an extension to robust output-feedback design based on noisy input-output data. Finally, we apply sum-of-squares methods to construct relaxation hierarchies for the considered robust controller design problem which are asymptotically exact. We illustrate through various examples that our approach provides a flexible framework for simultaneously leveraging prior knowledge and data, thereby reducing conservatism and improving performance significantly if compared to purely data-driven controller design.
TL;DR: A flexible performance-based control scheme, featuring the capability of avoiding the violation of the resulted modified performance functions (MPFs) due to the input saturation, is proposed, theoretically shown that the output can always track the reference signal and satisfy the constraints of the MPFs.
TL;DR: It is proved that the solution of the event-triggered Hamilton–Jacobi–Bellman (ETHJB) equation, which arises in the constrained optimal control problem, guarantees original system states to be uniformly ultimately bounded (UUB).
Abstract: In this paper, we study the event-triggered robust stabilization problem of nonlinear systems subject to mismatched perturbations and input constraints. First, with the introduction of an infinite-horizon cost function for the auxiliary system, we transform the robust stabilization problem into a constrained optimal control problem. Then, we prove that the solution of the event-triggered Hamilton–Jacobi–Bellman (ETHJB) equation, which arises in the constrained optimal control problem, guarantees original system states to be uniformly ultimately bounded (UUB). To solve the ETHJB equation, we present a single network adaptive critic design (SN-ACD). The critic network used in the SN-ACD is tuned through the gradient descent method. By using Lyapunov method, we demonstrate that all the signals in the closed-loop auxiliary system are UUB. Finally, we provide two examples, including the pendulum system, to validate the proposed event-triggered control strategy.