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Reinforcement learning aims to find policies that maximize an expected cumulative reward in Markov decision processes with unknown transition probabilities. Policy gradient (PG)-algorithms use stochastic gradients of the value function to update the policy. A major drawback of PG-algorithms is that they are limited to episodic tasks (multiple finite-horizon trajectories) unless stringent stationarity assumptions are imposed on the trajectories. Hence, they need restarts and cannot be fully implemented online, which is critical for systems need to adapt to new tasks and/or environments in deployment. Moreover, the standard stationary formulation ignores transient behaviors. This motivates our study of discounted MDPs of infinite horizon without restarts. However, it is unknown if in this case following stochastic PG-type estimates would improve the policy. The main result of this work is to establish that when policies belong to a reproducing kernel Hilbert space (RKHS), and the kernel is selected properly, then these PG-estimates are ascent directions for the value function conditioned to any arbitrary initial point. This allows us to prove convergence of our online algorithm to the local optima. A numerical example shows that an agent running our online algorithm learns to navigate and succeeds in a surveillance task that requires looping between two goal locations. This example corroborates our theoretical findings about the ascent directions of subsequent stochastic gradients. It also shows how our online algorithm guides the agent through a continuing cyclic trajectory that does not comply with the standard stationarity assumptions in the literature for non-episodic training. [ABSTRACT FROM AUTHOR]

The problem of an adaptive Lyapunov redesign is revisited for a class of systems without a priori knowledge of the function majoring nonlinear uncertainties and disturbances. An adaptive barrier function-based gain for unit control is proposed, ensuring an arbitrary a priori predefined uniform ultimate bound for solutions despite the presence of uncertainties and disturbances. The usage of positive semi-definite barrier function generates a continuous control signal adjusting the chattering, when the perturbations are decreasing to zero. [ABSTRACT FROM AUTHOR]

In this article, we rely on the theoretical foundations of radial basis function neural networks to form an adaptive parameter estimation problem, which we solve using the recently introduced prescribed performance control methodology. Such combination results in a compact user-configurable adaptive nonlinear system identification methodology that can be used to retrieve the open-loop nonlinear plant dynamics in any compact region of interest. [ABSTRACT FROM AUTHOR]

This article proposes a distributed error estimation approach to investigate the quasi-synchronization problem of heterogeneous dynamical networks with static and adaptive coupling laws under a directed communication topology. By introducing a pining control strategy, a novel class of distributed error estimation algorithms is proposed for solving the quasi-synchronization problem of heterogeneous dynamical networks with a static coupling law by exploring the local information among the neighboring nodes. By removing the assumption that the smallest real part of the nonzero eigenvalues of the Laplacian matrix associated with the communication graph must be known, we also address the case of the quasi-synchronization of heterogeneous dynamical networks with nonidentical nonlinear dynamics and an adaptive coupling law. It is proved, in the sense of Lyapunov function, that the distributed error estimation for the quasi-synchronization problem of heterogeneous dynamical networks with static and adaptive coupling laws will be achieved with a bounded synchronization error level. Finally, two examples are presented to demonstrate the effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

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 article, we introduce adaptive CBFs (aCBFs) that can accommodate time-varying control bounds and noise in the system dynamics while also guaranteeing the feasibility of the QPs if the original quadratic cost optimization problem itself is feasible, which is a challenging problem in current approaches. We propose two different types of aCBFs: parameter-adaptive CBF (PACBF) and relaxation-adaptive CBF (RACBF). Central to aCBFs 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 with their own auxiliary dynamics, which are stabilized by CLFs. We demonstrate the advantages of using aCBFs 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. [ABSTRACT FROM AUTHOR]

This article 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 normalized error based adaptive parameter 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 $\forall t\geq 0$ ; 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. [ABSTRACT FROM AUTHOR]

We study a class of heterodirectional semilinear hyperbolic partial differential equations, where the distributed state vector is partially measured. An observer estimating the unmeasured part of the state vector is designed. The design is, for instance, applicable to multiphase 1-D fluid models, where the pressure is measured, but the distributed flow and phase concentrations are not. Furthermore, the observer is extended to systems with parametric uncertainties appearing in the dynamics of the unmeasured part of the state. While required to be linear in the uncertain parameter, the uncertain term may be nonlinear in the state, even in the unmeasured part of the state. Terms of this type appear often in applications and cover, for instance, viscous drag in fluid flow systems. A noteworthy property of the design is that convergence of the state estimate is achieved without requiring persistent excitation. Two example applications are presented, and the design is illustrated in a simulation. [ABSTRACT FROM AUTHOR]

Current approaches to the cooperative control of network systems are based on a priori knowledge about the (follower) system dynamics: either the dynamics are known, or assumed to be minimum phase, or initial stabilizing controllers are available for each system. The purpose of this article is to show that for single-input single-output systems (SISO) the above assumptions can be relaxed. We propose an indirect adaptive methodology that does not require the knowledge of the parameters of the systems, or the systems to be minimum phase, or initial stabilizing controllers, in order to guarantee asymptotic tracking. [ABSTRACT FROM AUTHOR]

In this article, the problem of simultaneous leader–following consensus and parameter estimation is studied for a class of multiagent systems subject to an uncertain leader system. The leader system is described by a sum of sinusoids with unknown amplitudes, frequencies, and phases. A fully distributed adaptive observer is established for each agent to estimate the unknown frequencies of the leader without using any global information. It is shown that if the signal of the leader is sufficiently rich, the estimation errors of the unknown frequencies converge to zero asymptotically for all the agents. Based on the designed distributed adaptive observer, a distributed adaptive control law is synthesized for each agent to solve the leader–following consensus problem. [ABSTRACT FROM AUTHOR]

This article concerns the problem of adaptive output regulation for multivariable nonlinear systems in normal form. We present a regulator employing an adaptive internal model of the exogenous signals based on the theory of nonlinear Luenberger observers. Adaptation is performed by means of discrete-time system identification schemes, in which every algorithm fulfilling some optimality and stability conditions can be used. Practical and approximate regulation results are given relating the prediction capabilities of the identified model to the asymptotic bound on the regulated variables, which become asymptotic whenever a “right” internal model exists in the identifier's model set. The proposed approach, moreover, does not require “high-gain” stabilization actions. [ABSTRACT FROM AUTHOR]

This article addresses the decentralized tracking control problem for a class of strong interconnected nonlinear systems with actuator faults. The considered interconnections are allowed to be dominated by some bounding functions, which are linear growth in the status of all subsystems. First, an adaptive high-gain technique is introduced to deal with the unknown strong interconnections. Then, a group of fault-tolerant controllers is designed to adaptively compensate for the effects of the actuator failures, in which the controller gain parameters are adjusted online only according to local available information. Furthermore, with the aid of an algebraic graph theory result, it is proved that all signals of the closed-loop system are globally uniformly bounded, and the tracking errors of all subsystems converge to zero asymptotically. The effectiveness of the proposed control algorithm is demonstrated by a numerical simulation. [ABSTRACT FROM AUTHOR]

We prove the existence of a multidimensional nontrivial invariant toroidal manifold for the Kuramoto network with adaptive coupling. The constructed invariant manifold corresponds to the multicluster behavior of the oscillators phases. Contrary to the static coupling, the adaptive coupling strengths exhibit quasiperiodic oscillations preserving zero phase-difference within clusters. The derived sufficient conditions for the existence of the invariant manifold provide a tradeoff between the natural frequencies of the oscillators, coupling plasticity parameters, and the interconnection structure of the network. Furthermore, we study the robustness of the invariant manifold with respect to the perturbations of the interconnection topology, and establish structural, and quantitative constraints on the perturbation adjacency matrix preserving the invariant manifold. Additionally, we demonstrate the application of the new results to the problem of interconnection topology design, which consists in endowing the desired multicluster behavior to the network by controlling its interconnection structure. [ABSTRACT FROM AUTHOR]

This article considers the problem of output feedback funnel control for a class of uncertain nonlinear systems with arbitrary known relative degree. By utilizing the funnel control approach with a barrier Lyapunov function, a novel adaptive output feedback controller is constructed recursively, which accomplishes the output tracking with prescribed transient behavior. The developed control scheme features that the precise knowledge of system nonlinearities, including generally required bounding functions, is not needed. A physical example is performed to verify the effectiveness of the proposed theoretical findings. [ABSTRACT FROM AUTHOR]

This article deals with the problem of formulating an adaptive model-predictive control strategy for constrained uncertain systems. We consider a linear system in the presence of bounded time-varying additive uncertainty. The uncertainty is decoupled as the sum of a process noise with known bounds and a time-varying offset that we wish to identify. The time-varying offset uncertainty is assumed unknown pointwise in time. Its domain, called the feasible parameter set, and its maximum rate of change are known to the control designer. As new data become available, we refine the feasible parameter set with a set-membership-method-based approach, using the known bounds on process noise. We consider the case of probabilistic constraints on system states, with hard constraints on actuator inputs. We robustly satisfy the imposed constraints for all possible values of the offset uncertainty in the feasible parameter set. By imposing adequate terminal conditions, we prove recursive feasibility and stability of the proposed algorithm. The efficacy of the proposed approach is illustrated with a detailed numerical example. [ABSTRACT FROM AUTHOR]

This article considers the finite-time adaptive control problem of nonlinear systems with quantized input signal. Compared with existing results, the quantized parameters are unknown and the bound of the disturbance is not required. By utilizing the command filter backstepping method, an adaptive switching-type controller is designed and a novel switching mechanism is also proposed. By regulating the controller parameters online, practical finite-time stability can be guaranteed for the closed-loop system. Finally, a simulation example is given to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This article investigates global practical output tracking via adaptive output feedback for a class of uncertain nonlinear systems. Remarkably, the control problem under investigation is in the context of unknown control directions and output feedback, which severely restricts the system nonlinearities. Nevertheless, the growth on the unknown system nonlinearities in this article is extended from polynomial (of output) to arbitrary function, and meanwhile no further a priori information is required on the reference signal to be tracked. Specifically, sufficiently smooth pseudosign and pseudo-dead-zone functions are introduced acting as substitutions of sign and dead-zone functions in the literature, respectively. Typically, based on the pseudo-dead-zone function, a delicate estimate on the unknown system nonlinearities is established and a novel Lyapunov function is proposed. This, together with the elegant system performance analysis, is quite critical to remove the polynomial constraint and overcome the technical obstacle stemming from the essential extension. Additionally owing to the two refined functions, the use of smooth domination/treatment is moderately avoided in control design that enables the established control strategy to be tighter and less conservative. It turns out that under the proposed adaptive output-feedback controller, all the closed-loop system states are globally bounded, while the system tracking error enters a prescribed λ neighborhood of the origin in finite time and remains inside thereafter. A simulation example illustrates the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this article, we consider the problem of selecting important nodes in a random network, where the nodes connect to each other randomly with certain transition probabilities. The node importance is characterized by the stationary probabilities of the corresponding nodes in a Markov chain defined over the network, as in Google's PageRank. Unlike a deterministic network, the transition probabilities in a random network are unknown but can be estimated by sampling. Under a Bayesian learning framework, we apply the first-order Taylor expansion and normal approximation to provide a computationally efficient posterior approximation of the stationary probabilities. In order to maximize the probability of correct selection, we propose a dynamic sampling procedure, which uses not only posterior means and variances of certain interaction parameters between different nodes, but also the sensitivities of the stationary probabilities with respect to each interaction parameter. Numerical experiment results demonstrate the superiority of the proposed sampling procedure. [ABSTRACT FROM AUTHOR]

This article considers adaptive output-feedback control problem for nonsquare multi-input–multi-output systems (MIMO) with arbitrary relative degree. The proposed controller, based on the L1 adaptive control architecture, is designed using the right interactor matrix and a suitably defined projection matrix. A state-output predictor, a low-pass filter, and adaptive laws are introduced that achieve output tracking of a desired reference signal. It is shown that the proposed control strategy guarantees closed-loop stability with arbitrarily small steady-state errors. The transient performance in the presence of nonzero initialization errors is quantified in terms of decreasing functions. Rigorous mathematical analysis and illustrative examples are provided to validate the theoretical claims. [ABSTRACT FROM AUTHOR]

This article studies the infinite-horizon adaptive optimal control of continuous-time linear periodic (CTLP) systems. A novel value iteration (VI) based off-policy adaptive dynamic programming (ADP) algorithm is proposed for a general class of CTLP systems, so that approximate optimal solutions can be obtained directly from the collected data, without the exact knowledge of system dynamics. Under mild conditions, the proofs on uniform convergence of the proposed algorithm to the optimal solutions are given for both the model-based and model-free cases. The VI-based ADP algorithm is able to find suboptimal controllers without assuming the knowledge of an initial stabilizing controller. Application to the optimal control of a triple inverted pendulum subjected to a periodically varying load demonstrates the feasibility and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Contagious processes, such as spread of infectious diseases, social behaviors, or computer viruses, affect biological, social, and technological systems. Epidemic models for large populations and finite populations on networks have been used to understand and control both transient and steady-state behaviors. Typically it is assumed that after recovery from an infection, every agent will either return to its original susceptible state or acquire full immunity to reinfection. We study the network SIRI (Susceptible-Infected-Recovered-Infected) model, an epidemic model for the spread of contagious processes on a network of heterogeneous agents that can adapt their susceptibility to reinfection. The model generalizes existing models to accommodate realistic conditions in which agents acquire partial or compromised immunity after first exposure to an infection. We prove necessary and sufficient conditions on model parameters and network structure that distinguish four dynamic regimes: infection-free, epidemic, endemic, and bistable. For the bistable regime, which is not accounted for in traditional models, we show how there can be a rapid resurgent epidemic after what looks like convergence to an infection-free population. We use the model and its predictive capability to show how control strategies can be designed to mitigate problematic contagious behaviors. [ABSTRACT FROM AUTHOR]

This article investigates adaptive state-feedback stabilization problem for a class of stochastic high-order nonlinear systems with unknown time-varying powers and stochastic inverse dynamics for the first time. The existence of stochastic inverse dynamics, unknown parameters, and time-varying powers makes stochastic high-order nonlinear systems essentially different from the related papers, which brings a series of obstacles to achieve the control objective. By virtue of the parameter separation principle, adaptive technique and some flexible algebraic methods, a novel adaptive state-feedback controller is designed to guarantee that the equilibrium of the closed-loop system is globally stable in probability. Finally, a simulation is provided to demonstrate the effectiveness of the control scheme. [ABSTRACT FROM AUTHOR]

This article deals with the problem of output regulation in a “nonequilibrium” context for a special class of multivariable nonlinear systems stabilizable by high-gain feedback. A postprocessing internal model design suitable for the multivariable nature of the system, which might have more inputs than regulation errors, is proposed. Uncertainties in the system and exosystem are dealt with by assuming that the ideal steady-state input belongs to a certain “class of signals,” by which an appropriate model set for the internal model can be derived. The adaptation mechanism for the internal model is then cast as an identification problem, and a least-squares solution is specifically developed. In line with recent developments in the field, the vision that emerges from this article is that approximate, possibly asymptotic, regulation is the appropriate way of approaching the problem in a multivariable and uncertain context. New insights about the use of identification tools in the design of adaptive internal models are also presented. [ABSTRACT FROM AUTHOR]

This note proposes a new extended-state observer-based framework for an adaptive nonlinear regulator design of a class of nonlinear systems, in the general nonequilibrium theory. By augmenting an adaptive extended-state observer with an internal model, one is able to obtain an estimate of the term containing uncertain parameters, which then makes it possible to design an adaptive internal model in the presence of a general nonlinearly parameterized immersion condition. [ABSTRACT FROM AUTHOR]

This paper considers the problem of designing adaptive feedforward control (AFC) systems for uncertain single-input single-output linear systems perturbed by multisinusoidal disturbances of known frequencies. The proposed approach removes the longstanding assumption that either the sign of the real part or the imaginary part of the transfer function of a stable plant at the frequency of excitation is known for AFC to be applicable, which is referred to in this paper as a strictly positive real (SPR)-like condition. Notable features of the solution are that persistence of excitation is not required, and stability analysis tools based on averaging are avoided; hence, the requirement of an exponentially stable equilibrium for the closed-loop system is circumvented. [ABSTRACT FROM AUTHOR]

In this technical note, an adaptive model-predictive control (MPC) is proposed for a class of discrete-time linear systems with constant parametric uncertainties and control constraint. The proposed adaptive MPC originates from the principle of min–max optimization, which cannot be solved in a direct numerical way. An adaptive strategy is proposed to estimate the uncertain parameters, such that the estimated error converges, and the optimization in the MPC can be transferred into a solvable simple structure. Feasibility of the optimization and stability of the closed-loop system are proved theoretically, and a simulation example is presented to illustrate the theoretical result. [ABSTRACT FROM AUTHOR]

This paper focuses on the problem of global finite-time stabilization for a class of uncertain nonlinear systems with event-triggered inputs. The existing event-based design methods can only partially compensate for the effects of the event-triggered errors and cannot completely counteract them to achieve finite-time control. For this reason, a new method about event triggering mechanism and event-triggered controller codesign is presented based on the idea of backstepping design and the sign function technique. It is proved that the event-triggered control system is the Zeno-free and the newly proposed control strategy ensures the global finite-time stability of the closed-loop systems via Lyapunov analyses and finite-time stability theory, which improves the existing results of only boundedness or asymptotic stability. Finally, two examples are performed to demonstrate the validity of the proposed strategy. [ABSTRACT FROM AUTHOR]

This paper presents an improved backstepping control implementation scheme for a $n$ -dimensional strict-feedback uncertain nonlinear system based on command filtered backstepping and adaptive neural network backstepping. In this approach, $n$ command filters and one neural network are applied to reconstruct the approximations of unknown nonlinearities, which are related to the system uncertainties including the system's unmodeled dynamics and external disturbances. Then, one can use the negative feedback of these approximations to compensate the system uncertainties. Moreover, convex optimization and soft computing technique are adopted to design the update law of the weights of the neural network, and Lyapunov stability criterion is used to prove the stability of the closed-loop system. Finally, simulation results are given to show the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper considers the adaptive error feedback regulation problem for a one-dimensional heat equation with general harmonic disturbance anticollocated with control. We first construct an auxiliary system in which the control and the anticollocated disturbance become collocated and the measured error becomes the output. Then, we design an error feedback adaptive servomechanism for this system, which includes estimators for the parameters characterizing the disturbance and the reference signals. The control is thus designed to regulate the tracking error to zero and keep the states bounded. [ABSTRACT FROM AUTHOR]

This paper proposes a robust self-triggered model predictive control (MPC) with an adaptive prediction horizon scheme for constrained nonlinear discrete-time systems subject to additive disturbances. At each triggering instant, the controller provides an optimal control sequence by solving an optimal control problem (OCP), and at the same time, determines the next triggering time and prediction horizon. By implementing the algorithm, the average sampling frequency is reduced and the prediction horizon is adaptively decreased as the system state approaches a terminal region. Meanwhile, an upper bound of performance loss is guaranteed when compared with a nominal periodic sampling MPC. Feasibility of the OCP and stability of the closed-loop system are established. Simulation results verify the effectiveness of the scheme. [ABSTRACT FROM AUTHOR]

Reinforcement learning (RL) has been successfully employed as a powerful tool in designing adaptive optimal controllers. Recently, off-policy learning has emerged to design optimal controllers for systems with completely unknown dynamics. However, current approaches for optimal tracking control design either result in bounded tracking error, rather than zero tracking error, or require partial knowledge of the system dynamics. Moreover, they usually require to collect a large set of data to learn the optimal solution. To obviate these limitations, this paper applies a combination of off-policy learning and experience-replay for output regulation tracking control of continuous-time linear systems with completely unknown dynamics. To this end, the off-policy integral RL-based technique is first used to obtain the optimal control feedback gain, and to explicitly identify the involved system dynamics using the same data. Second, a data-efficient-based experience replay method is developed to compute the exosystem dynamics. Finally, the output regulator equations are solved using data measured online. It is shown that the proposed control method stabilizes the closed-loop tracking error dynamics, and gives an explicit exponential convergence rate for the output tracking error. Simulation results show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

The problem of global finite-time stabilization for $p$ -normal nonlinear systems subject to uncertain time-varying control coefficients and vanishing nonlinear uncertainties without homogeneous growth restriction is investigated in this paper. By virtue of the technique of homogeneous domination, a new dual-layer adaptive approach is presented to address the uncertainties and nonlinearities of the system. For one layer of the adaptive mechanism, a nonlinear adaptive parameter estimator is proposed to reconstruct the upper bounds of the unknown uncertainties. For the other, an explicit construction approach of a new adaptive dynamic gain mechanism is presented for the first time to cope with the uncertain time-varying control coefficients of the $p$ -normal nonlinear systems. It is shown that the global boundedness of the systems under consideration is guaranteed by the presented approach, and in addition the time taken to converge to the equilibrium is rendered to be finite time. [ABSTRACT FROM AUTHOR]

This technical note considers the dynamic average consensus problem, where a group of networked agents are required to estimate the average of their time-varying reference signals. Almost all existing solutions to this problem require a specific initialization of the estimator states, and such constraints render the algorithms vulnerable to network disruptions. Here, we present three robust algorithms that do not entail any initialization criteria. Furthermore, the proposed algorithms do not rely on the full knowledge of the dynamics generating the reference signals nor assume access to its time derivatives. Two of the proposed algorithms focus on undirected networks and make use of an adaptive scheme that removes the explicit dependence of the algorithm on any upper bounds on the reference signals or its time derivatives. The third algorithm presented here provides a robust solution to the dynamic average consensus problem on directed networks. Compared to the existing algorithms for directed networks, the proposed algorithm guarantees an arbitrarily small steady-state error bound that is independent of any bounds on the reference signals or its time derivatives. The current formulation allows each agent to select its own performance criteria, and the algorithm parameters are distributedly selected such that the most stringent requirement among them is satisfied. A performance comparison of the proposed approach to existing algorithms is presented. [ABSTRACT FROM AUTHOR]

An adaptive algorithm solving the on-line parameter estimation problem for a broad class of linear systems is proposed. The approach can be applied to systems with delay, distributed-parameter systems, fractional-order systems, and others that are stable or stabilized by linear feedback. The proposed scheme can be applied to simultaneously track sufficiently slow changes in process gains, delays, time constants, diffusivity, and other parameters. The proposed method is gradient-based, and it yields a relatively efficient numerical implementation. Convergence and robustness of the algorithm are investigated through Lyapunov analysis, yielding explicit convergence conditions that generalize the well-known “persistence of excitation” and identifiability requirements arising in conventional adaptive estimation. The method is illustrated by several examples. [ABSTRACT FROM AUTHOR]

This paper addresses the event-triggered tracking for a class of uncertain nonlinear systems. Essentially different from the related works, the nonlinear systems allow serious (parametric) uncertainties, while no further a priori information, excepting some coarse information, is required on the reference signal to be tracked. This makes event-triggered control more challenging, partially because the sampling error cannot be precisely bounded any more. As main contributions of this paper, new adaptive event-triggered tracking schemes are proposed for the systems in two event-triggering architectures with different roles of the event-triggering mechanism on the information transmitting and control computing/updating. Much importantly, a dynamic gain is incorporated in either scheme not only to counteract the serious uncertainties, but also to overcome the bad influence of the sampling error. Based on the dynamic gain, two adaptive event-triggered controllers are designed with distinct event-triggering mechanisms, respectively. Particularly, to ensure application flexibility, one of the triggering mechanisms is rendered relatively independent of the controller signal. The designed event-triggered controllers are shown to achieve the practical tracking for the systems, that is, the prespecified arbitrary tracking accuracy can be guaranteed (a comparable objective to that via continuous-time control), while avoiding infinitely fast sampling/execution. [ABSTRACT FROM AUTHOR]

Stabilization of linear systems with unknown dynamics is a canonical problem in adaptive control. Since the lack of knowledge of system parameters can cause it to become destabilized, an adaptive stabilization procedure is needed prior to regulation. Therefore, the adaptive stabilization needs to be completed in finite time. In order to achieve this goal, asymptotic approaches are not very helpful. There are only a few existing nonasymptotic results and a full treatment of the problem is not currently available. In this paper, leveraging the novel method of random linear feedbacks, we establish high probability guarantees for finite-time stabilization. Our results hold for remarkably general settings because we carefully choose a minimal set of assumptions. These include stabilizability of the underlying system and restricting the degree of heaviness of the noise distribution. To derive our results, we also introduce a number of new concepts and technical tools to address regularity and instability of the closed-loop matrix. [ABSTRACT FROM AUTHOR]

In this note, we propose a novel adaptive fixed-time control scheme for output tracking problems of a class of multi-input multi-output (MIMO) nonlinear systems with asymmetric output constraint requirements, using a new universal barrier function. It is universal in the sense that the proposed scheme is a general one that also works for systems with symmetric constraints or without constraint requirements, without changing the control structure. Novel adaptive estimations and analysis are introduced to address system uncertainties in the fixed-time convergence settings. We show that under the proposed novel control scheme, each element in the system output tracking error vector of the MIMO nonlinear system can converge into small sets near zero with fixed-time convergence rate, while the asymmetric output constraint requirements on each element of the output tracking error are satisfied at all time. The proposed scheme can effectively deal with unmatched system uncertainties and uncertain gain functions. In the end, a simulation example on a two-degree-of-freedom robot manipulator is presented to demonstrate the efficacy of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper generalizes the LaSalle–Yoshizawa Theorem to switched nonsmooth systems. The Filippov and Krasovskii regularizations of a switched system are shown to be contained within the convex hull of the Filippov and Krasovskii regularizations of the subsystems, respectively. A common candidate Lyapunov function that has a negative semidefinite generalized time derivative along the trajectories of the subsystems is shown to be sufficient to establish LaSalle–Yoshizawa-like results for the switched system. Of independent interest, are the results on approximate continuity and Filippov regularization of set-valued maps, reduction of differential inclusions using Lipschitz continuous regular functions, and comparative remarks on different generalizations of the time derivative along the trajectories of a nonsmooth system. [ABSTRACT FROM AUTHOR]

Global adaptive stabilization by partial state feedback is studied for time-delay cascade systems with nonlinear parameterization. The inverse-dynamics of time-delay nonlinear systems under consideration is of a lower-triangular form and assumed to satisfy certain ISS-like conditions. By taking advantage of the lower-triangular structure, we present an iterative algorithm for changing supply rates so that the time-delay zero-dynamics can be handled effectively. With the aid of the iterative technique of changing supply rates, we develop a dynamic gain-based control strategy that, together with the feedback domination design, leads to a construction of partial-state, delay-free adaptive controllers. As a result, all the states of the time-delay cascade system are regulated to the origin and the boundedness of the solution of the closed-loop system is achieved. [ABSTRACT FROM AUTHOR]

This paper develops an adaptive actuator failure compensation control scheme for discrete-time and possibly nonminimum-phase systems with unknown actuator failures of characterizations that first, some unknown system inputs are stuck at some unknown fixed or varying values at unknown time instants, and second, the actuator failures as system disturbances are not matched by other inputs. Such a failure compensation control problem is solved by using a new control separation design based on a new linear quadratic (LQ) control formulation: One control component is used for disturbance rejection and actuator failure compensation, and one component is used for closed-loop stability and regulation, to achieve the desired control objective. The nominal LQ control solution uses a new cost function to derive the two-component control signal, which has improved performance over a traditional LQ control design. The adaptive actuator failure compensation control problem is solved using a stable adaptive law for parameter estimation, to guarantee the system stability and output regulation performances in the presence of plant and actuator failure uncertainties. Simulation results are presented to verify the satisfactory performance of the proposed adaptive LQ control scheme. [ABSTRACT FROM AUTHOR]

In this paper, we will analyze a basic class of diffusion adaptive filters based on least mean squares algorithms. Both stability and performance analyses will be carried out under a general cooperative information condition, without such stringent conditions as statistical independence and stationarity that have been used in almost all the existing literature and, thus, makes our theory applicable to stochastic systems with feedback. In comparison with the existing work, a key theoretical difficulty that needs to be overcome in this paper is to analyze the product of asymmetric correlated nonstationary random matrices, which is inherent in the structure of the diffusion-type filtering algorithms. We will further demonstrate that the distributed adaptive filters can estimate a dynamic process of interest from noisy measurements by a set of sensors working in a cooperative way, in the natural scenario where none of the sensors can fulfill the estimation task individually due to insufficient information. Finally, the necessity of our cooperative information condition will also be discussed in this paper. [ABSTRACT FROM AUTHOR]

For continuous-discrete filtering with unpredictable approximation errors, by proposing the novel stochastic feedback scheme, this note elaborates a closed-loop adaptive Kalman filter for nonlinear continuous-discrete systems. In conventional filters, unknown approximation errors might arise due to the integration/discretization and linearization of continuous model, and ruin the optimality of Kalman theory. As the main contribution of this note, the stochastic feedback based covariance adaption scheme does not require the approximation steps; instead, the posteriori sequence is mined as a feedback to adapt the priori error covariance, so that the unpredictable errors and costly calculations can be reduced or controlled in the novel closed-loop filtering structure. The new approach's advantages in computational cost, adaptability, and accuracy have been demonstrated by the numerical simulations. [ABSTRACT FROM AUTHOR]

Coalitional control is concerned with the management of multi-agent systems where cooperation cannot be taken for granted (due to, e.g., market competition, logistics). This paper proposes a model predictive control (MPC) framework aimed at large-scale dynamically coupled systems whose individual components, possessing a limited model of the system, are controlled independently, pursuing possibly competing objectives. The emergence of cooperating clusters of controllers is contemplated through an autonomous negotiation protocol, based on the characterization as a coalitional game of the benefit derived by a broader feedback and the alignment of the individual objectives. Specific mechanisms for the cooperative benefit redistribution that relax the cognitive requirements of the game are employed to compensate for possible local cost increases due to cooperation. As a result, the structure of the overall MPC feedback can be adapted online to the degree of interaction between different parts of the system while satisfying the individual interests of the agents. A wide-area control application for the power grid with the objective of minimizing frequency deviations and undesired interarea power transfers is used as a study case. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of secure state estimation for cyber-physical systems modeled by continuous or discrete-time linear systems when some sensors are corrupted by an attacker. A novel state observer is proposed with adaptive switching mechanism. Attack tolerance principle is established based on adaptively truncating the injection channels of attacks. To implement it, a switching function matrix is introduced into the observer design. Driven by a well-defined performance index, the switching function matrix automatically reaches and remains in the desired entry mode and turns off the input channels of attacks. Based on the equivalence between $s$ -strong detectability of the observation error system and $2s$ -sparse detectability of the original system, the observation error system is proven to be asymptotically stable even under the cyber attacks. Compared with the existing complex static batch optimization algorithms, the proposed adaptive observer can be derived only by offline solving a set of simple linear matrix inequalities. Simulation examples are given to illustrate the estimation performance and the computational efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

This technical note establishes a novel result for adaptive asymptotic tracking control of uncertain switched linear systems. The result exploits a recently proposed stability condition for switched systems. In particular, a time-varying positive definite Lyapunov function is used to develop a novel piecewise continuous model-reference adaptive law and a dwell-time switching law. In contrast with previous research, where asymptotic tracking was possible only in the presence of a common Lyapunov function for the reference models, in this work asymptotic tracking is shown in a more general setting. Additionally, in the presence of persistence of excitation, the controller parameter estimation errors will converge to zero asymptotically. The main contribution of this work consists in establishing a symmetry between adaptive control of classical non-switched linear systems and adaptive control of switched linear systems. A practical example with an electro-hydraulic system is adopted to illustrate the results. [ABSTRACT FROM AUTHOR]

We propose an adaptive observer scheme to estimate boundary parameters in first-order hyperbolic systems of Partial Differential Equations (PDE). The considered systems feature an arbitrary number of states traveling in one direction and one counter-convecting state. Uncertainties in the boundary reflection coefficients and boundary additive errors are estimated relying on a pre-existing observer design and a novel Lyapunov-based adaptation law. [ABSTRACT FROM AUTHOR]

Estimating disturbances/unknown inputs of a given system is an important technique that finds various engineering and industrial applications. Two such examples are the so-called disturbance-observer-based control and fault detection/isolation. The traditional design of a disturbance/unknown input observer (DOB/UIOB) usually involves utilizing the inverse of the model of the open-loop system. Hence, such design can only be applied to systems with stable, or “minimal phase”, zeros. In this manuscript, we propose a novel adaptive observer for estimating the unknown and nearly periodic input of a linear-time-invariant (LTI) single-input-single-output (SISO) discrete-time system. The observer assumes the form of an adaptive FIR filter whose coefficients are obtained based on the given system model via the least-squares algorithm with the covariance matrix reset. An important advantage of the proposed approach is that the approach does not involve inverting the open-loop system model; therefore, it can be successfully applied to both minimum-phase and non-minimum phase systems. The effectiveness of the proposed observer design is assessed by a numerical example. [ABSTRACT FROM AUTHOR]