Showing papers on "Separation principle published in 2021"

Observer-Based Neuro-Adaptive Optimized Control of Strict-Feedback Nonlinear Systems With State Constraints

Abstract: This article proposes an adaptive neural network (NN) output feedback optimized control design for a class of strict-feedback nonlinear systems that contain unknown internal dynamics and the states that are immeasurable and constrained within some predefined compact sets. NNs are used to approximate the unknown internal dynamics, and an adaptive NN state observer is developed to estimate the immeasurable states. By constructing a barrier type of optimal cost functions for subsystems and employing an observer and the actor-critic architecture, the virtual and actual optimal controllers are developed under the framework of backstepping technique. In addition to ensuring the boundedness of all closed-loop signals, the proposed strategy can also guarantee that system states are confined within some preselected compact sets all the time. This is achieved by means of barrier Lyapunov functions which have been successfully applied to various kinds of nonlinear systems such as strict-feedback and pure-feedback dynamics. Besides, our developed optimal controller requires less conditions on system dynamics than some existing approaches concerning optimal control. The effectiveness of the proposed optimal control approach is eventually validated by numerical as well as practical examples.

LQG Control and Sensing Co-Design

Abstract: We investigate a linear-quadratic-Gaussian (LQG) control and sensing codesign problem, where one jointly designs sensing and control policies. We focus on the realistic case where the sensing design is selected among a finite set of available sensors, where each sensor is associated with a different cost (e.g., power consumption). We consider two dual problem instances: sensing-constrained LQG control, where one maximizes a control performance subject to a sensor cost budget, and minimum-sensing LQG control, where one minimizes a sensor cost subject to performance constraints. We prove that no polynomial time algorithm guarantees across all problem instances a constant approximation factor from the optimal. Nonetheless, we present the first polynomial time algorithms with per-instance suboptimality guarantees. To this end, we leverage a separation principle, which partially decouples the design of sensing and control. Then, we frame LQG codesign as the optimization of approximately supermodular set functions; we develop novel algorithms to solve the problems; and we prove original results on the performance of the algorithms and establish connections between their suboptimality and control-theoretic quantities. We conclude the article by discussing two applications, namely, sensing-constrained formation control and resource-constrained robot navigation .

Observer-Based Spacecraft Formation Coordinated Control via a Unified Event-Triggered Communication

Abstract: This article addresses the formation tracking control problem for multiple spacecraft systems subject to limited communication resources and external disturbances. Considering that only a subset of the follower spacecraft can have access to the motion states of the dynamic leader, an event-based distributed observer is first developed to reconstruct the leader's information. Subsequently, to achieve the accompanying flight of the follower spacecraft around the leader with a desired formation configuration, for each follower spacecraft, a distributed event-triggered coordinated controller is proposed. In particular, by embedding simultaneously the position information and observer output into the triggering function, a novel unified event-triggered mechanism is designed to schedule information transmission in multiple spacecraft systems. The salient characters of the distributed coordinated control scheme are twofold: unnecessary occupancy of communication resources can be avoided significantly; and asymptotic stability of the whole closed-loop system is guaranteed without resorting to the separation principle. Finally, numerical simulations are carried out to illustrate the efficiency of the theoretical results.

A Two-Degree-of-Freedom Controller Design Satisfying Separation Principle with Fractional Order PD and Generalized ESO

Abstract: This paper proposes a two-degree-of-freedom fractional-order proportional-derivative (FOPD) controller with a general extended state observer (GESO) to achieve both optimal speed tracking and disturbance rejection performance for a typical permanent magnet synchronous motor (PMSM) servo system. The GESO simplifies the control plant, estimates and actively rejects total disturbances. The FOPD controller achieves fast speed tracking with almost no overshoot. Furthermore, it is verified that the control system with the proposed FOPD-GESO controller design meets the separation principle through mathematical derivation and simulation illustration. It shows that the proposed controller breaks the inherent trade-off on tracking performance and disturbance robustness of the typical traditional PID control. Meanwhile, a systematic scheme for designing the FOPD-GESO controller to satisfy both frequency-domain and time-domain specifications is proposed in this paper. Simulation illustration and experimental validation are performed to demonstrate that the proposed FOPD-GESO controller is superior to the typical integer-order PID (IOPID) controller and integer order active disturbance rejection control (IOADRC) with a typical extended state observer in terms of speed tracking, anti-load disturbance and robustness to internal uncertainties.

Decentralized Control for Networked Control Systems with Asymmetric Information

Abstract: This paper considers the decentralized control for networked control systems (NCSs) with asymmetric partial information sharing between two controllers. In this NCSs model, the controller 2 (C2) shares its observations and part of its historical control inputs with the controller 1 (C1), whereas C2 cannot obtain the information of C1 due to network constraints. Under the linear control strategies assumption, we present the optimal estimators for C1 and C2 respectively. It is noted that the estimation error covariance (EEC) is coupled with the controller which means that the classical separation principle fails. By applying the Pontryagin's maximum principle, we obtain a solution to the forward and backward stochastic difference equations. Based on this solution, we derive the optimal controllers. Combining the linear optimal controllers with the EEC, the controller C1 is decoupled from the EEC. It should be emphasized that the control gain is dependent on the estimation gain. Moreover, the estimation gain satisfies the forward Riccati equation and the control gain satisfies the backward Riccati equation. We propose iterative solutions to the Riccati equ

Mixed PD-Type Iterative Learning Control Algorithm for a Class of Parabolic Singular Distributed Parameter Systems

Abstract: In this paper, the iterative learning control (ILC) problem is investigated for a class of time-invariant parabolic singular distributed parameter systems. Initially, the singular distributed parameter systems is decomposed into infinite number of singular systems based on the separation principle. Meanwhile, the slow-fast subsystems are introduced via singular value decomposition method. Then, a novel mixed PD-type ILC algorithm with finite dimension is designed for the low dimensional slow part and the corresponding convergence conditions are manifested. With the proposed controller, the output error of high dimensional fast complement can satisfy the given value instead of neglecting the effect of high dimensional modes. Furthermore, under the aforesaid ILC law and the appropriate number of the low dimensional slow part, the resulting tracking error of parabolic singular distributed parameter systems can converge to any small tracking accuracy. Finally, simulation results on the distributed building automatic temperature system verify the convergence and effectiveness of the mixed PD-type ILC algorithm.

A Distributed Luenberger Observer for Linear State Feedback Systems With Quantized and Rate-Limited Communications

Abstract: This article addresses the problem of simultaneous distributed state estimation, and control of linear systems with linear state feedback, subjected to process, and measurement noise, under the constraints of quantized, and rate-limited network data transmission. In the set-up adopted, sensors and actuators communicate through a network with a strongly connected topology. Unlike the case of centralized linear systems, for which the separation principle holds, the above practical assumption prevents the separate design of observers, and controller because each of the nodes does not necessarily have access to the control inputs generated at all the other nodes. We derive a linear distributed Luenberger observer, and a set of sufficient conditions that guarantee ultimate boundedness of the estimation error, and system state vectors, with bounds that depend on the $\mathcal {L}_{\infty }$ norm of the noise signals, and the number of bits used in the transmissions. A numerical example illustrates the performance and effectiveness of the proposed algorithm in controlling a network of open-loop unstable systems.

Integrated sensor fault estimation and control for continuous-time switched systems: A new separation principle.

Abstract: In this paper, we address the state/fault estimation and observer-based control issues for switched systems with sensor faults. The main objective is to estimate sensor faults and compensate for their effects on the system state estimation, and then stabilize the switched system by the estimated state feedback. Applying the mode-dependent average dwell time (MDADT) concept and the Lyapunov stability theory, a new separation principle is developed, which allows formalizing the observer-based controller design in the form of linear matrix inequalities (LMI) instead of bilinear ones. Finally, a highly manoeuvrable aircraft technology (HiMAT) example, a DC–DC boost converter example, and a numerical example are investigated to show the practicability and efficiency of the obtained results.

Output Feedback Synthesis of Multi-Agent Systems with Jointly Connected Switching Networks: A Separation Principle Approach

Abstract: The paper presents distributed output feedback synthesis for both leaderless consensus and leader-follower consensus of linear multi-agent systems subject to jointly connected switching networks. Luenberger type distributed observers are proposed based on the neighborhood output estimation error, and distributed output feedback controllers are developed according to the certainty equivalence principle. To show uniform global exponential stability of the switched closed-loop system, a separation principle for a class of switched linear systems with a cascaded structure is established employing weak Lyapunov function and checking weak zero-state detectability of its ‘`diagonal’' switched subsystems. It is shown that the weak zero-state detectability can be guaranteed by a generalized uniform joint-connected condition of switching networks without any dwell-time constraints.

MPPT Control Paradigms for PMSG-WECS: A Synergistic Control Strategy With Gain-Scheduled Sliding Mode Observer

Abstract: The wind energy conversion system (WECS) frequently operates under highly stochastic and unpredictable wind speed. Thus, the maximum power (MP) extraction, in such unpredictable scenarios, becomes a very appealing control objective. This paper focuses on the extraction of MP from a variable-speed WECSs, which further drive a permanent magnet synchronous generator (PMSG). At the first stage, the dynamical model of the PMSG is converted into Bronwsky form, which is comprised of both visible and internal dynamics. The first-order internal dynamics are proved stable, i.e., the system is minimum phase. The control of the second-order visible dynamics, to track a varying profile of the wind speed, is the main consideration. This job is accomplished via Backstepping-based robust Sliding Mode Control (SMC) strategy. Since, a conventional SMC suffers from inherited chattering issue, thus, the discontinuous control component in SMC scheme is replaced with super-twisting and real-twisting control laws. In addition, the immeasurable states’ information are estimated via gain-scheduled sliding mode observer. The overall closed-loop stability is ensured by analysing the quasi-linear form, which supports the separation principle. The theoretical claims are authenticated via simulation results, which are performed in Matlab/Simulink environment. Besides, a comparative analysis is carried out with the standard literature results, which quite obviously outshines the investigated control approaches in terms of varying wind profile tracking and the corresponding control input.

Linear-quadratic-Gaussian mean-field-game with partial observation and common noise

Abstract: This paper considers a class of linear-quadratic-Gaussian (LQG) mean-field games (MFGs) with partial observation structure for individual agents. Unlike other literature, there are some special features in our formulation. First, the individual state is driven by some common-noise due to the external factor and the state-average thus becomes a random process instead of a deterministic quantity. Second, the sensor function of individual observation depends on state-average thus the agents are coupled in triple manner: not only in their states and cost functionals, but also through their observation mechanism. The decentralized strategies for individual agents are derived by the Kalman filtering and separation principle. The consistency condition is obtained which is equivalent to the wellposedness of some forward-backward stochastic differential equation (FBSDE) driven by common noise. Finally, the related \begin{document}$ \epsilon $\end{document} -Nash equilibrium property is verified.

Output Regulation of Linear Stochastic Systems

Abstract: We address the output regulation problem for a general class of linear stochastic systems. Specifically, we formulate and solve the ideal full-information and output-feedback problems, obtaining perfect, but non-causal, asymptotic regulation. A characterisation of the problem solvability is deduced. We point out that the ideal problems cannot be solved in practice because they unrealistically require that the Brownian motion affecting the system is available for feedback. Drawing from the ideal solution, we formulate and solve approximate versions of the full-information and output-feedback problems, which do not yield perfect asymptotic tracking but can be solved in a realistic scenario. These solutions rely on two key ideas: first we introduce a discrete-time a-posteriori estimator of the variations of the Brownian motion obtained causally by sampling the system state or output; second we introduce a hybrid state observer and a hybrid regulator scheme which employ the estimated Brownian variations. The approximate solution tends to the ideal as the sampling period tends to zero. The proposed theory is validated by the regulation of a circuit subject to electromagnetic noise.

Portfolio diversification and model uncertainty: A robust dynamic mean-variance approach

Abstract: This paper focuses on a dynamic multi-asset mean-variance portfolio selection problem under model uncertainty. We develop a continuous time framework for taking into account ambiguity aversion about both expected return rates and correlation matrix of the assets, and for studying the join effects on portfolio diversification. The dynamic setting allows us to consider time varying ambiguity sets, which include the cases where the drift and correlation are estimated on a rolling window of historical data or when the investor takes into account learning on the ambiguity. In this context, we prove a general separation principle for the associated robust control problem, which allows us to reduce the determination of the optimal dynamic strategy to the parametric computation of the minimal risk premium function. Our results provide a justification for under-diversification, as documented in empirical studies and in the static models [16], [34]. Furthermore, we explicitly quantify the degree of under-diversification in terms of correlation bounds and Sharpe ratios proximities, and emphasize the different features induced by drift and correlation ambiguity. In particular, we show that an investor with a poor confidence in the expected return estimation does not hold any risky asset, and on the other hand, trades only one risky asset when the level of ambiguity on correlation matrix is large. We also provide a complete picture of the diversification for the optimal robust portfolio in the three-asset case JEL Classification: G11, C61 MSC Classification: 91G10, 91G80, 60H30

Iterative Solution of Linear Matrix Inequalities for the Combined Control and Observer Design of Systems with Polytopic Parameter Uncertainty and Stochastic Noise

Abstract: Most research activities that utilize linear matrix inequality (LMI) techniques are based on the assumption that the separation principle of control and observer synthesis holds. This principle states that the combination of separately designed linear state feedback controllers and linear state observers, which are independently proven to be stable, results in overall stable system dynamics. However, even for linear systems, this property does not necessarily hold if polytopic parameter uncertainty and stochastic noise influence the system’s state and output equations. In this case, the control and observer design needs to be performed simultaneously to guarantee stabilization. However, the loss of the validity of the separation principle leads to nonlinear matrix inequalities instead of LMIs. For those nonlinear inequalities, the current paper proposes an iterative LMI solution procedure. If this algorithm produces a feasible solution, the resulting controller and observer gains ensure robust stability of the closed-loop control system for all possible parameter values. In addition, the proposed optimization criterion leads to a minimization of the sensitivity to stochastic noise so that the actual state trajectories converge as closely as possible to the desired operating point. The efficiency of the proposed solution approach is demonstrated by stabilizing the Zeeman catastrophe machine along the unstable branch of its bifurcation diagram. Additionally, an observer-based tracking control task is embedded into an iterative learning-type control framework.

Observer-Based Robust Control Method for Switched Neutral Systems in the Presence of Interval Time-Varying Delays

Abstract: In this study, the challenges of the controller design of a class of Uncertain Switched Neutral Systems (USNSs) in the presence of discrete, neutral, and time-varying delays are considered by using a robust observer-based control technique. The cases where the uncertainties are normbounded and time-varying are emphasized in this research. The adopted control approach reduces the prescribed level of disturbance input on the controlled output in the closed-loop form and the robust exponential stability of the control system. The challenge of parametric uncertainty in USNSs is solved by designing a robust output observer-based control and applying the Yakubovich lemma. Since the separation principle does not generally hold in this research, the controller and observer cannot be designed separately, sufficient conditions are suggested. These conditions are composed of applying the average dwell time approach and piecewise Lyapunov function technique in terms of linear matrix inequalities, which guarantees robust exponential stability of the observer-based output controller. Finally, two examples are given to determine the effectiveness of the proposed method.

Global Distributed Attitude Tracking Control of Multiple Rigid Bodies via Quaternion-Based Hybrid Feedback

Abstract: This article investigates the leader-following attitude tracking control problem of multiple rigid body systems in the presence of uncertain parameters and disturbances. The communication constraint is considered that only a subset of followers have access to the leader, and a quaternion-based nonlinear hybrid distributed observer is first proposed to estimate the leader's trajectory for each follower. In particular, the proposed distributed attitude observer always evolves on the 3-D unit sphere $\mathbb {S}^{3}$ . This property guarantees the feasibility of the observer-based distributed control scheme, since the separation principle is satisfied. By incorporating a hysteresis-based switch of a binary logic variable for each pair of neighboring rigid bodies, the proposed hybrid distributed observer achieves the global asymptotic stability for any initial attitude and avoids the unwinding phenomenon. Next, an observer-based attitude tracking control law is developed by combining adaptive technique and hybrid theory, which does not require precise model information and has good robustness to the disturbances. In addition, it is shown that the attitude tracking errors converge to the origin globally asymptotically. Finally, simulation results are provided to validate the theoretical results.

Parametric output regulation using observer-based PI controllers with applications in flexible spacecraft attitude control

Abstract: A parametric multiobjective design approach based on a proportional-integral (PI) controller and a full-state observer is proposed for output regulation in a multivariable linear system. First, a complete parametric form of the observer-based PI control law is established, which yields a closed-loop system with the desired eigenstructure and ensures that the regulated output asymptotically tracks a given constant signal in the presence of constant but unknown disturbances. All design degrees of freedom are preserved and characterized using a set of parameter vectors. Second, a separation principle of eigenvalue sensitivities is proven, and based on this result, the parameters of the closed-loop system are comprehensively optimized to reduce the eigenvalue sensitivity and the control gain, and also to enhance the tolerance to time-varying disturbances. Finally, the proposed method is applied to attitude control of a flexible spacecraft. Moreover, numerical simulations based on practical engineering parameters are performed to verify the superiority of the proposed method over traditional proportional-integral-derivative (PID) control methods.

Output Feedback Control for Irregular LQ Problem

Abstract: In this letter, we study the irregular output feedback linear quadratic (LQ) control problem where the state is measured through a linear system with noise. It is interesting to show that the irregular output feedback control with the standard average LQ cost is unsolvable even if the state feedback LQ control is solvable, which is completely different from the classical regular output feedback LQ control. In order to guarantee the solvability of the irregular output feedback control, the LQ cost is modified at the terminal time with the expectation of terminal state in this letter. In the framework of the modified cost function, it is shown that the separation principle holds and the explicitly optimal controller is given in the feedback form of the Kalman filtering. In particular, the feedback gain is calculated by two Riccati equations, independently of the Kalman filtering. The key technique is the analytical solution of the forward and backward differential equations (FBDEs). We also emphasize that the optimal controller at the terminal time is required to be deterministic.

Partial Diffusion Markov Model of Heterogeneous TCP Link: Optimization with Incomplete Information

Abstract: The paper presents a new mathematical model of TCP (Transmission Control Protocol) link functioning in a heterogeneous (wired/wireless) channel. It represents a controllable, partially observable stochastic dynamic system. The system state describes the status of the modeled TCP link and expresses it via an unobservable controllable MJP (Markov jump process) with finite-state space. Observations are formed by low-frequency counting processes of packet losses and timeouts and a high-frequency compound Poisson process of packet acknowledgments. The information transmission through the TCP-equipped channel is considered a stochastic control problem with incomplete information. The main idea to solve it is to impose the separation principle on the problem. The paper proposes a mathematical framework and algorithmic support to implement the solution. It includes a solution to the stochastic control problem with complete information, a diffusion approximation of the high-frequency observations, a solution to the MJP state filtering problem given the observations with multiplicative noises, and a numerical scheme of the filtering algorithm. The paper also contains the results of a comparative study of the proposed state-based congestion control algorithm with the contemporary TCP versions: Illinois, CUBIC, Compound, and BBR (Bottleneck Bandwidth and RTT).