Showing papers in "IEEE Transactions on Automatic Control in 2021"

Data-Driven Model Predictive Control With Stability and Robustness Guarantees

Abstract: We propose a robust data-driven model predictive control (MPC) scheme to control linear time-invariant systems. The scheme uses an implicit model description based on behavioral systems theory and past measured trajectories. In particular, it does not require any prior identification step, but only an initially measured input–output trajectory as well as an upper bound on the order of the unknown system. First, we prove exponential stability of a nominal data-driven MPC scheme with terminal equality constraints in the case of no measurement noise. For bounded additive output measurement noise, we propose a robust modification of the scheme, including a slack variable with regularization in the cost. We prove that the application of this robust MPC scheme in a multistep fashion leads to practical exponential stability of the closed loop w.r.t. the noise level. The presented results provide the first (theoretical) analysis of closed-loop properties, resulting from a simple, purely data-driven MPC scheme.

Push–Pull Gradient Methods for Distributed Optimization in Networks

Abstract: In this article, we focus on solving a distributed convex optimization problem in a network, where each agent has its own convex cost function and the goal is to minimize the sum of the agents’ cost functions while obeying the network connectivity structure. In order to minimize the sum of the cost functions, we consider new distributed gradient-based methods where each node maintains two estimates, namely an estimate of the optimal decision variable and an estimate of the gradient for the average of the agents’ objective functions. From the viewpoint of an agent, the information about the gradients is pushed to the neighbors, whereas the information about the decision variable is pulled from the neighbors, hence giving the name “push–pull gradient methods.” The methods utilize two different graphs for the information exchange among agents and, as such, unify the algorithms with different types of distributed architecture, including decentralized (peer to peer), centralized (master–slave), and semicentralized (leader–follower) architectures. We show that the proposed algorithms and their many variants converge linearly for strongly convex and smooth objective functions over a network (possibly with unidirectional data links) in both synchronous and asynchronous random-gossip settings. In particular, under the random-gossip setting, “push–pull” is the first class of algorithms for distributed optimization over directed graphs. Moreover, we numerically evaluate our proposed algorithms in both scenarios, and show that they outperform other existing linearly convergent schemes, especially for ill-conditioned problems and networks that are not well balanced.

Adaptive Event-Triggered Consensus of Multiagent Systems on Directed Graphs

Abstract: This article systematically studies consensus of linear multiagent systems (MASs) on directed graphs through adaptive event-triggered control. It presents innovative adaptive event-triggered state-feedback protocols with novel composite event-triggering conditions. Two specific designs in terms of different event-triggering conditions and laws of adaption are first discussed for linear MASs on strongly connected directed graphs, which are then extended to general directed graphs that contain a spanning tree. Moreover, another adaptive event-triggered protocol is proposed for solving leader–follower consensus that tracks a leader of a bounded control input. The protocols inherit the merits of both adaptive control and event-triggered control: the protocols can be implemented in a fully distributed way, since the Laplacian is avoided in design, and each agent only needs to know the relative information between neighbors at discrete instants determined by event-triggering conditions. Compared with the existing related results, the proposed protocols are applicable for linear MASs on general directed graphs, and moreover, the time-dependent term in the event-triggering conditions is allowed to be a class of positive $L_1$ functions. Two numerical examples clearly verify the effectiveness of the proposed protocols.

Adaptive Finite-Time Stabilization of Stochastic Nonlinear Systems Subject to Full-State Constraints and Input Saturation

Abstract: In this article, the adaptive finite-time tracking control is studied for state constrained stochastic nonlinear systems with parametric uncertainties and input saturation. To this end, a definition of semiglobally finite-time stability in probability (SGFSP) is presented and a related stochastic Lyapunov theorem is established and proved. To alleviate the serious uncertainties and state constraints, the adaptive backstepping control and barrier Lyapunov function are combined in a unified framework. Then, by applying a function approximation method and the auxiliary system method to deal with input saturation respectively, two adaptive state-feedback controllers are constructed. Based on the proposed stochastic Lyapunov theorem, each constructed controller can guarantee the closed-loop system achieves SGFSP, the system states remain in the defined compact sets and the output tracks the reference signal very well. Finally, a stochastic single-link robot system is established and used to demonstrate the effectiveness of the proposed schemes.

Distributed Observer-Based Cooperative Control Approach for Uncertain Nonlinear MASs Under Event-Triggered Communication

Abstract: The distributed tracking problem for uncertain nonlinear multi-agent systems (MASs) under event-triggered communication is an important issue. However, existing results only provide solutions that can only ensure stability with bounded tracking errors, as asymptotic tracking is difficult to be achieved mainly due to the errors caused by eventtriggering mechanisms and system uncertainties. In this work, with the aim of overcoming such difficulty, we propose a new methodology. The subsystems in MASs are divided into two groups, in which the first group consists of the subsystems that can access partial output of the reference system and the second one contains all the remaining subsystems. To estimate the state of the reference system, a new distributed eventtriggered observer is firstly designed for the first group based on a combined output observable condition. Then, a distributed eventtriggered observer is proposed for the second group by employing the observer state of the first group. Based on the designed observers, adaptive controllers are derived for all subsystems. It is established that global stability of the closed loop system is ensured and asymptotic convergence of all the tracking errors is achieved. Moreover, a simulation example is provided to show the effectiveness of the proposed method.

Bipartite Consensus Tracking for Second-Order Multiagent Systems: A Time-Varying Function-Based Preset-Time Approach

Abstract: This article is concerned with bipartite consensus tracking for second-order multiagent systems with signed directed graphs. A time-varying function-based preset-time approach is proposed to realize the convergence in predetermined time. First, a class of time-varying functions with generalized properties are presented. Second, two time-varying function-based auxiliaries and a corresponding manifold are constructed. Under a structurally balanced and strongly connected graph, a time-varying function-based controller considering the neighboring state is proposed to guarantee that the system trajectory is constrained on the manifold such that bipartite consensus tracking is achieved in preset-time. Third, for first-order multiagent systems, a preset-time controller is further developed with simplified design. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed controllers.

Distributionally Robust Chance Constrained Data-enabled Predictive Control

Abstract: We study the problem of finite-time constrained optimal control of unknown stochastic linear time-invariant systems, which is the key ingredient of a predictive control algorithm - albeit typically having access to a model. We propose a novel distributionally robust data-enabled predictive control (DeePC) algorithm which uses noise-corrupted input/output data to predict future trajectories and compute optimal control inputs while satisfying output chance constraints. The algorithm is based on (i) a non-parametric representation of the subspace spanning the system behaviour, where past trajectories are sorted in Page or Hankel matrices; and (ii) a distributionally robust optimization formulation which gives rise to strong probabilistic performance guarantees. We show that for certain objective functions, DeePC exhibits strong out-of-sample performance, and at the same time respects constraints with high probability. The algorithm provides an end-to-end approach to control design for unknown stochastic linear time-invariant systems. We illustrate the closed-loop performance of the DeePC in an aerial robotics case study.

Event-Based Formation Control for Nonlinear Multiagent Systems Under DoS Attacks

Abstract: This article focuses on the formation control problem of nonlinear multiagent systems under denial-of-service attacks. The formation control can be preserved by the distributed hybrid event-triggering strategies (HETSs). As a balance between periodic and continuous event-triggering strategies, HETS arranges a tradeoff between the resource utilization and the communication frequency among agents. Theoretical results are verified using a benchmark problem of six miniature quadrotor prototypes.

A Computationally Efficient Robust Model Predictive Control Framework for Uncertain Nonlinear Systems

Abstract: In this article, we present a nonlinear robust model predictive control (MPC) framework for general (state and input dependent) disturbances. This approach uses an online constructed tube in order to tighten the nominal (state and input) constraints. To facilitate an efficient online implementation, the shape of the tube is based on an offline computed incremental Lyapunov function with a corresponding (nonlinear) incrementally stabilizing feedback. Crucially, the online optimization only implicitly includes these nonlinear functions in terms of scalar bounds, which enables an efficient implementation. Furthermore, to account for an efficient evaluation of the worst case disturbance, a simple function is constructed offline that upper bounds the possible disturbance realizations in a neighborhood of a given point of the open-loop trajectory. The resulting MPC scheme ensures robust constraint satisfaction and practical asymptotic stability with a moderate increase in the online computational demand compared to a nominal MPC. We demonstrate the applicability of the proposed framework in comparison to state-of-the-art robust MPC approaches with a nonlinear benchmark example.

Stochastic Nonlinear Prescribed-Time Stabilization and Inverse Optimality

Abstract: We solve the prescribed-time mean-square stabilization and inverse optimality control problems for stochastic strict-feedback nonlinear systems by developing a new non-scaling backstepping design scheme. A key novel design ingredient is that the time-varying function is not used to scale the coordinate transformations and is only suitably introduced into the virtual controllers. The advantage of this approach is that a simpler controller results and the control effort is reduced. By using this method, we design a new controller to guarantee that the equilibrium at the origin of the closed-loop system is prescribed-time mean-square stable. Then, we redesign the controller and solve the prescribed-time inverse optimal mean-square stabilization problem, with an infinite gain margin. Specifically, the designed controller is not only optimal with respect to a meaningful cost functional but also globally stabilizes the closed-loop system in the prescribed-time. Finally, two simulation examples are given to illustrate the stochastic nonlinear prescribed-time control design.

From noisy data to feedback controllers: non-conservative design via a matrix S-lemma

Abstract: We propose a new method to obtain feedback controllers of an unknown dynamical system directly from noisy input/state data. The key ingredient of our design is a new matrix S-lemma that will be proven in this paper. We provide both strict and non-strict versions of this S-lemma, that are of interest in their own right. Thereafter, we will apply these results to data-driven control. In particular, we will derive non-conservative design methods for quadratic stabilization, H_2 and H_inf control, all in terms of data-based linear matrix inequalities. In contrast to previous work, the dimensions of our decision variables are independent of the time horizon of the experiment. Our approach thus enables control design from large data sets.

A Novel Framework for Backstepping-Based Control of Discrete-Time Strict-Feedback Nonlinear Systems With Multiplicative Noises

Abstract: This article is concerned with the exponential mean-square stabilization problem for a class of discrete-time strict-feedback nonlinear systems subject to multiplicative noises. The state-dependent multiplicative noise is assumed to occur randomly based on a stochastic variable obeying the Gaussian white distribution. To tackle the difficulties caused by the multiplicative noise, a novel backstepping-based control framework is developed to design both the virtual control laws and the actual control law for the original nonlinear system, and such a framework is fundamentally different from the traditional $n$ -step predictor strategy. The proposed design scheme provides an effective way in establishing the relationship between the system states and the controlled errors, by which a noise-intensity-dependant stability condition is derived to ensure that the closed-loop system is exponentially mean-square stable for exactly known systems. To further cope with nonlinear modeling uncertainties, the radial basis function neural network (NN) is employed as a function approximator. In virtue of the proposed backstepping-based control framework, the ideal controller is characterized as a function of all system states, which is independent of the virtual control laws. Therefore, only one NN is employed in the final step of the backstepping procedure and, subsequently, a novel adaptive neural controller (with modified weight updating laws) is presented to ensure that both the neural weight estimates and the system states are uniformly bounded in the mean-square sense under certain stability conditions. The control performance of the proposed scheme is illustrated through simulation results.

Formal Synthesis of Stochastic Systems via Control Barrier Certificates

Abstract: This article focuses on synthesizing control policies for discrete-time stochastic control systems together with a lower bound on the probability that the systems satisfy the complex temporal properties. The desired properties of the system are expressed as linear temporal logic specifications over finite traces. In particular, our approach decomposes the given specification into simpler reachability tasks based on its automata representation. We, then, propose the use of so-called control barrier certificate to solve those simpler reachability tasks along with computing the corresponding controllers and probability bounds. Finally, we combine those controllers to obtain a hybrid control policy solving the considered problem. Under some assumptions, we also provide two systematic approaches for uncountable and finite input sets to search for control barrier certificates. We demonstrate the effectiveness of the proposed approach on a room temperature control and lane keeping of a vehicle modeled as a four-dimensional single-track kinematic model. We compare our results with the discretization-based methods in the literature.

Polynomial-Type Lyapunov–Krasovskii Functional and Jacobi–Bessel Inequality: Further Results on Stability Analysis of Time-Delay Systems

Abstract: To derive a less conservative stability criterion via Lyapunov-Krasovskii functional (LKF) method, in previous literature, multiple integral terms are usually introduced into the construction of LKFs. This article generalizes the results of previous literature by proposing a polynomial-type LKF, which contains the LKFs with multiple integral terms as special cases. In addition, a Jacobi–Bessel inequality is presented to bound the derivative of such LKF. As a result, an improved stability criterion of time-delay systems is established. Finally, two numerical examples are given to illustrate the effectiveness, and advantages of our method.

New Results on Parameter Estimation via Dynamic Regressor Extension and Mixing: Continuous and Discrete-Time Cases

Abstract: We present some new results on the dynamic regressor extension and mixing parameter estimators for linear regression models recently proposed in the literature. This technique has proven instrumental in the solution of several open problems in system identification and adaptive control. The new results include the following, first, a unified treatment of the continuous and the discrete-time cases; second, the proposal of two new extended regressor matrices, one which guarantees a quantifiable transient performance improvement , and the other exponential convergence under conditions that are strictly weaker than regressor persistence of excitation; and, third, an alternative estimator ensuring convergence in finite-time whose adaptation gain, in contrast with the existing one, does not converge to zero. Simulations that illustrate our results are also presented.

Networked Control Under DoS Attacks: Tradeoffs Between Resilience and Data Rate

Abstract: In this article, we study communication-constrained networked control problems for linear time-invariant systems in the presence of Denial-of-Service (DoS) attacks, namely attacks that prevent transmissions over the communication network. Our article aims at exploring the tradeoffs between system resilience and network bandwidth capacity. Given a class of DoS attacks, we characterize the bit-rate conditions that are dependent on the unstable eigenvalues of the dynamic matrix of the plant and the parameters of DoS attacks, under which exponential stability of the closed-loop system can be guaranteed. Our characterization clearly shows the tradeoffs between the communication bandwidth and resilience against DoS. An example is given to illustrate the proposed approach.

Decentralized Proximal Gradient Algorithms With Linear Convergence Rates

Abstract: This article studies a class of nonsmooth decentralized multiagent optimization problems where the agents aim at minimizing a sum of local strongly-convex smooth components plus a common nonsmooth term. We propose a general primal-dual algorithmic framework that unifies many existing state-of-the-art algorithms. We establish linear convergence of the proposed method to the exact minimizer in the presence of the nonsmooth term. Moreover, for the more general class of problems with agent specific nonsmooth terms, we show that linear convergence cannot be achieved (in the worst case) for the class of algorithms that uses the gradients and the proximal mappings of the smooth and nonsmooth parts, respectively. We further provide a numerical counterexample that shows how some state-of-the-art algorithms fail to converge linearly for strongly convex objectives and different local non smooth terms.

Reverse and Forward Engineering of Local Voltage Control in Distribution Networks

Abstract: The increasing penetration of renewable and distributed energy resources in distribution networks calls for real-time and distributed voltage control. In this article, we investigate local Volt/VAR control with a general class of control functions, and show that the power system dynamics with nonincremental local voltage control can be seen as a distributed algorithm for solving a well-defined optimization problem (reverse engineering). The reverse engineering further reveals a fundamental limitation of the nonincremental voltage control: the convergence condition is restrictive and prevents better voltage regulation at equilibrium. This motivates us to design two incremental local voltage control schemes based on the subgradient and pseudo-gradient algorithms, respectively, for solving the same optimization problem (forward engineering). The new control schemes decouple the dynamical property from the equilibrium property, and have much less restrictive convergence conditions. This article presents another step toward developing a new foundation—network dynamics as optimization algorithms—for distributed real-time control and optimization of future power networks.

Robustness for Stability and Stabilization of Boolean Networks With Stochastic Function Perturbations

Abstract: In genetic regulatory networks (GRNs), gene mutations often occur in a stochastic manner. As an important model of GRNs, gene mutations of Boolean networks are always described as function perturbations. This article studies the robust stability and stabilization of Boolean networks with stochastic function perturbations. A kind of parameterized set is constructed, and it is revealed that under the stochastic function perturbations, the property of finite-time stability remains unchanged when the perturbed set and the parameterized set are disjoint. In addition, it is proved that the finite-time stability is reduced to stability in distribution when the intersection of perturbed set and complement set of parameterized set is nonempty. As an application, the robust stabilization problem of Boolean control networks with stochastic function perturbations is discussed, and several necessary and sufficient conditions are presented for the robustness of feedback stabilizers. Finally, the obtained results are used to study the Drosophila melanogaster segmentation polarity gene network and the lac operon in the bacterium Escherichia coil.

Distributed Online Optimization for Multi-Agent Networks With Coupled Inequality Constraints

Abstract: This article investigates the distributed online optimization problem over a multi-agent network subject to local set constraints and coupled inequality constraints, which has a lot of applications in many areas, such as wireless sensor networks, power systems, and plug-in electric vehicles. In this problem, the cost function at each time step is the sum of local cost functions with each of them being gradually revealed to its corresponding agent, and meanwhile only local functions in coupled inequality constraints are accessible to each agent. To address this problem, a modified primal-dual algorithm, called distributed online primal-dual push-sum algorithm, is developed in this article, which does not rest on any assumption on parameter boundedness and is applicable to unbalanced networks. It is shown that the proposed algorithm is sublinear for both the dynamic regret and the violation of coupled inequality constraints. Finally, the theoretical results are supported by a simulation example.

Adaptive Asymptotic Tracking with Global Performance for Nonlinear Systems with Unknown Control Directions

Abstract: This note presents a global adaptive asymptotic tracking control method, capable of guaranteeing prescribed transient behavior for uncertain strict-feedback nonlinear systems with arbitrary relative degree and unknown control directions. Unlike most existing funnel controls that are built upon time-varying feedback gains, the proposed method is derived from a tracking error-dependent normalized function and a barrier function, together with a time-varying scaling transformation, leading to an improved prescribed performance control solution with the following features: 1) the developed control is embedded with adaptive tuning and is able to ensure asymptotic tracking; 2) given transient performance is guaranteed in that the tracking error preserves in the prescribed boundary for $\forall t\ge 0$ ; and 3) it is able to cope with nonlinear systems with arbitrary relative degree, mismatched uncertainties and unknown control directions. Both theoretical analysis and numerical simulations verify the effectiveness and benefits of the proposed method.

A Novel Outlier-Robust Kalman Filtering Framework Based on Statistical Similarity Measure

Abstract: In this article, a statistical similarity measure is introduced to quantify the similarity between two random vectors. The measure is, then, employed to develop a novel outlier-robust Kalman filtering framework. The approximation errors and the stability of the proposed filter are analyzed and discussed. To implement the filter, a fixed-point iterative algorithm and a separate iterative algorithm are given, and their local convergent conditions are also provided, and their comparisons have been made. In addition, selection of the similarity function is considered, and four exemplary similarity functions are established, from which the relations between our new method and existing outlier-robust Kalman filters are revealed. Simulation examples are used to illustrate the effectiveness and potential of the new filtering scheme.

Command Filter Adaptive Asymptotic Tracking of Uncertain Nonlinear Systems with Time-Varying Parameters and Disturbances

Abstract: This paper is devoted to the adaptive asymptotic tracking for a class of uncertain nonlinear systems. The presence of unknown time-varying parameters and uncertain disturbances makes the systems in question essentially different from those in the related works. By skillfully combining adaptive technique and command filter-based backstepping, a novel command filter adaptive tracking controller is successfully designed to achieve asymptotic tracking. The typical feature of the proposed controller lies in the introduction of a smooth function with positive integrable time-varying function, which makes the controller powerful enough to compensate the unknown time-varying parameters and uncertain disturbances. Remarkably, a novel Lyapunov function by incorporating the lower bounds of control gains is used to prove the stability of the closed-loop system. Compared with some existing command filter-based backstepping, the conditions on the virtual control coefficients and disturbances are relaxed. Finally, the effectiveness of the proposed method is shown by a simulation example.

Ultimately Bounded Filtering Subject to Impulsive Measurement Outliers

Abstract: This paper is concerned with the ultimately bounded filtering problem for linear time-delay systems subject to norm-bounded disturbances and impulsive measurement outliers (IMOs). The considered IMOs are modeled by a sequence of impulsive signals with certain known minimum norm (i.e. the minimum of the norms of all impulsive signals). In order to characterize the occasional occurrence of IMOs, a sequence of independently and identically distributed random variables is introduced to depict the interval lengths (i.e. the durations between two adjacent IMOs) of the outliers. In order to achieve satisfactory filtering performance, a novel parameter-dependent filtering approach is proposed to protect the filtering performance from IMOs by using a special outlier detection scheme, which is developed based on a particular input-output model. The ultimate boundedness (in mean square) of the filtering error is investigated by using the stochastic analysis technique and Lyapunov-functional-like method. The desired filter gain matrix is derived through solving a constrained optimization problem. A simulation example is provided to demonstrate the effectiveness of our proposed

High Order Control Barrier Functions

Abstract: We approach the problem of stabilizing a dynamical system while optimizing a cost and satisfying safety and control constraints. For affine control systems and quadratic costs, it has been shown that Control Barrier Functions (CBF) guaranteeing safety and Control Lyapunov Functions (CLF) enforcing convergence can be used to reduce the optimal control problem to a sequence of Quadratic Programs. In this paper, we propose High Order CBFs (HOCBF), which can accommodate systems of arbitrary relative degree. We construct a set of controls that renders the intersection of a set of sets forward invariant for the system, which implies the satisfaction of the original safety constraint. Our notion of HOCBF is more general than the recently proposed exponential CBF. We formulate optimal control problems with constraints given by HOCBF and CLF, and propose two methods - the penalty and the parameterization methods - to address the feasibility problem. Finally, we show how our methodology can be extended for safe navigation in unknown environments with long-term feasibility. We illustrate the proposed framework on a cruise control system and on a robot control problem.

Optimism-Based Adaptive Regulation of Linear-Quadratic Systems

Abstract: The main challenge for adaptive regulation of linear-quadratic systems is the tradeoff between identification and control. An adaptive policy needs to address both the estimation of unknown dynamics parameters (exploration), as well as the regulation of the underlying system (exploitation). To this end, optimism-based methods that bias the identification in favor of optimistic approximations of the true parameter are employed in the literature. A number of asymptotic results have been established, but their finite-time counterparts are few, with important restrictions. This article establishes results for the worst-case regret of optimism-based adaptive policies. The presented high probability upper bounds are optimal up to logarithmic factors. The nonasymptotic analysis of this article requires the following very mild assumptions: stabilizability of the system's dynamics, and limiting the degree of heaviness of the noise distribution. To establish such bounds, certain novel techniques are developed to comprehensively address the probabilistic behavior of dependent random matrices with heavy-tailed distributions.

Moving-Horizon Estimation for Linear Dynamic Networks With Binary Encoding Schemes

Abstract: This article is concerned with moving-horizon state estimation problems for a class of discrete-time linear dynamic networks. The signals are transmitted via noisy network channels and distortions can be caused by channel noises. As such, the binary encoding schemes, which take advantages of the robustness of the binary data, are exploited during the signal transmission. More specifically, under such schemes, the original signals are encoded into a bit string, transmitted via memoryless binary symmetric channels with certain crossover probabilities, and eventually restored by a decoder at the receiver. Novel centralized and decentralized moving-horizon estimators in the presence of the binary encoding schemes are constructed by solving the respective global and local least-square optimization problems. Sufficient conditions are obtained through intensive stochastic analysis to guarantee the stochastically ultimate boundedness of the estimation errors. A simulation example is presented to verify the effectiveness of the proposed moving-horizon estimators.

Stochastic Adaptive Nonlinear Control With Filterless Least Squares

Abstract: For stochastic strict-feedback nonlinear systems with unknown parameters in the drift terms or the diffusion terms, we develop new least-squares identification schemes without regressor filtering. A key new ingredient in the proposed estimator design is a weighted term with design parameters, which is introduced to deal with the nonlinear terms and stochastic noise. With such an estimator, new adaptive controllers are designed to guarantee that the equilibrium at the origin of the closed-loop system is globally stable in probability, and the states are regulated to zero almost surely. Besides, by suitably selecting the estimator parameters, we prove that the proposed least-squares estimators are convergent, as well as strongly consistent in some special cases. Finally, two simulation examples are given to illustrate the least-squares identification and the adaptive control design.

A Hybrid Dynamic Event-Triggered Approach to Consensus of Multiagent Systems With External Disturbances

Abstract: This article addresses the event-triggered consensus problem of multiagent systems (MAS) with disturbances. Model-based control protocols are designed, and a hybrid dynamic event-triggering mechanism (HDETM) is proposed. Based on the proposed event-triggered control protocol, continuous communication between neighboring agents is not needed, and a prespecified strictly positive minimum ETI is guaranteed, i.e., Zeno behavior is excluded. A timer variable with jump dynamics is introduced to describe the HDETM in the closed-loop system. Then, a novel hybrid model is constructed for the closed-loop MAS, which contains both flow dynamics, and jump dynamics. Lyapunov-based stability analysis and HDETM design are presented based on hybrid systems framework, and matrix inequality conditions are given to verify the consensus and $\mathcal {H}_{\infty }$ performance. Finally, a spacecraft formation example is provided to show the effectiveness of the proposed methods.

Adaptive Control Barrier Functions

Abstract: It has been shown that optimizing quadratic costs while stabilizing affine control systems to desired (sets of) states subject to state and control constraints can be reduced to a sequence of Quadratic Programs (QPs) by using Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs). In this paper, we introduce Adaptive CBFs (AdaCBFs) that can accommodate time-varying control bounds and noise in the system dynamics,while also guaranteeing the feasibility of the QPs, which is a challenging problem in current approaches. We propose two different types of AdaCBFs: Parameter-Adaptive CBF (PACBF) and Relaxation-Adaptive CBF (RACBF). Central to AdaCBFs is the introduction of appropriate time-varying functions to modify the definition of a common CBF. These time-varying functions are treated as High Order CBFs (HOCBFs) with their own auxiliary dynamics, which are stabilized by CLFs. We demonstrate the advantages of using AdaCBFs over the existing CBF techniques by applying both the PACBF-based method and the RACBF-based method to a cruise control problem with time-varying road conditions and noise in the system dynamics, and compare their relative performance