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Various efforts have been devoted to developing stabilizing distributed model predictive control (MPC) schemes for tracking piecewise constant references. In these schemes, terminal sets are usually computed offline and used in the MPC online phase to guarantee recursive feasibility and asymptotic stability. Maximal invariant terminal sets do not necessarily respect the distributed structure of the network, hindering the distributed implementation of the controller. On the other hand, ellipsoidal terminal sets respect the distributed structure, but may lead to conservative schemes. In this article, a novel distributed MPC scheme is proposed for reference tracking of networked dynamical systems, where the terminal ingredients are reconfigured online depending on the closed-loop states to alleviate the aforementioned issues. The resulting nonconvex infinite-dimensional problem is approximated using a quadratic program. The proposed scheme is tested in simulation, where the proposed MPC problem is solved using distributed optimization. [ABSTRACT FROM AUTHOR]

This article focuses on the problem of prescribed-time control for a class of uncertain nonlinear systems. First, a prescribed-time stability theorem is proposed by following the adaptive technology for the first time. Based on this theorem, a new state feedback control strategy is put forward by using the backstepping method for high-order nonlinear systems with unknown parameters to ensure the prescribed-time convergence. Moreover, the prescribed-time controller is obtained in the form of continuous time-varying feedback, which can render all system states converge to zero within the prescribed time. It should be noted that the prescribed time is independent of system initial conditions, which means that the prescribed time can be set arbitrarily within the physical limitations. Finally, two simulation examples are provided to illustrate the effectiveness of our proposed algorithm. [ABSTRACT FROM AUTHOR]

This article addresses reconfiguration-based fault-tolerant control (FTC) with robust guaranteed performance for nonlinear uncertain systems under actuator faults. A PAssive/ACTive combined FTC method is proposed based on reliable control, which synthesizes the advantages of the active and passive FTC and strikes a balance between the performance and complexity of the method. Moreover, the reliability overcost of this method is reduced to balance the system nominal performance and reconfigurability. In this procedure, the $\theta$ -D method is used to solve the Hamilton–Jacobi–Bellman (HJB) and generalized HJB equations. Effectiveness of the proposed method is verified by a numerical example. [ABSTRACT FROM AUTHOR]

This article presents a new parameter estimation algorithm for the adaptive control of a class of time-varying plants. The main feature of this algorithm is a matrix of time-varying learning rates, which enables parameter estimation error trajectories to tend exponentially fast toward a compact set whenever excitation conditions are satisfied. This algorithm is employed in a large class of problems where unknown parameters are present and are time-varying. It is shown that this algorithm guarantees global boundedness of the state and parameter errors of the system, and avoids an often used filtering approach for constructing key regressor signals. In addition, intervals of time over which these errors tend exponentially fast toward a compact set are provided, both in the presence of finite and persistent excitation. A projection operator is used to ensure the boundedness of the learning rate matrix, as compared to a time-varying forgetting factor. Numerical simulations are provided to complement the theoretical analysis. [ABSTRACT FROM AUTHOR]

This article proposes a method for enlarging the region of attraction of linear model predictive controllers (MPC) when tracking piecewise-constant references in the presence of pointwise-in-time constraints. It consists of an add-on unit, the feasibility governor (FG), that manipulates the reference command so as to ensure that the optimal control problem that underlies the MPC-feedback law remains feasible. Offline polyhedral projection algorithms based on multiobjective linear programming are employed to compute the set of feasible states and reference commands. Online, the action of the FG is computed by solving a convex quadratic program. The closed-loop system is shown to satisfy constraints, be asymptotically stable, exhibit zero-offset tracking, and display finite-time convergence of the reference. [ABSTRACT FROM AUTHOR]

The problem of global output tracking is addressed for stable minimum phase systems, with constant uncertain parameters and constant disturbances belonging to a known compact set, in the presence of input constraints such as amplitude saturation. The relative degree, the system order, and the sign of the high frequency gain are assumed to be known. A hybrid adaptive output feedback control is designed to achieve global asymptotic output tracking, provided that there exists an input within the input constraints capable of tracking exactly the output reference signal. By virtue of the hybrid control approach, the closed-loop system is linear within each time interval between parameter updating. Moreover, no information on input saturation is required by the controller. In addition to the standard assumptions in adaptive control design when inputs are unconstrained, further requirements on the reference signals, on system stability and on parameter bounds, are needed when inputs are constrained. [ABSTRACT FROM AUTHOR]

We propose algorithms for performing model checking and control synthesis for discrete-time uncertain systems under linear temporal logic (LTL) specifications. We construct temporal logic trees (TLTs) from LTL formulae via reachability analysis. In contrast to automaton-based methods, the construction of the TLT is abstraction-free for infinite systems; that is, we do not construct discrete abstractions of the infinite systems. Moreover, for a given transition system and an LTL formula, we prove that there exist both a universal TLT and an existential TLT via minimal and maximal reachability analysis, respectively. We show that the universal TLT is an underapproximation for the LTL formula and the existential TLT is an overapproximation. We provide sufficient conditions and necessary conditions to verify whether a transition system satisfies an LTL formula by using the TLT approximations. As a major contribution of this work, for a controlled transition system and an LTL formula, we prove that a controlled TLT can be constructed from the LTL formula via a control-dependent reachability analysis. Based on the controlled TLT, we design an online control synthesis algorithm, under which a set of feasible control inputs can be generated at each time step. We also prove that this algorithm is recursively feasible. We illustrate the proposed methods for both finite and infinite systems and highlight the generality and online scalability with two simulated examples. [ABSTRACT FROM AUTHOR]

The state-of-the-art quadratic-program-based control Lyapunov-barrier function (QP-CLBF) is a powerful control approach to balance safety and stability in an optimal fashion. However, under this approach, modeling inaccuracies may degrade the performance of closed-loop systems and cause violation or restriction of safety-critical constraints. This article presents an adaptive QP-CLBF approach for a class of nonlinear systems in the presence of parameter uncertainties with an unknown control coefficient. We begin by presenting a filtering-based concurrent learning (FCL) adaptive technique to guarantee simultaneous exponential convergence of system parameters and control coefficient. The proposed FCL extends and encompasses the baseline concurrent learning technique, which was developed to achieve exponential convergence of either system parameters exclusively or control coefficient while relying on the estimation of state derivatives using numerical smoothing. The proposed FCL adaptive method is then unified with a modified version of QP-CLBF to achieve exponential convergence of system parameters, control coefficient, and control Lyapunov and control barrier functions while establishing safety with the largest safe region. Under this unification, all results are exponential in the presence of modeling error without the need for numerical methods to estimate state derivatives. This is formally proven by employing a Lyapunov argument. Simulations are finally carried out to validate the theoretical results. [ABSTRACT FROM AUTHOR]

This technical article addresses the formation stabilization problem for multiagent systems (MASs) composed of dynamical agents moving within an obstacle-cluttered environment and sharing information via nonideal wireless communication networks. A novel distributed cooperative navigation function based control strategy is proposed, which drives the MAS to a desired formation without any collision while counteracting the presence of unavoidable communication impairments originated by the wireless network. By recasting the formation stabilization problem into a consensus one and by combining the Lyapunov stability theory with Halanay’s lemma, uniformly ultimately bounded stability of the whole delayed closed-loop system is proved. In the special case of an obstacle-free environment, our approach guarantees exponential stability of the closed-loop networked system. The stability analysis also provides an estimation of the delay upper bound and allows to evaluate the stability margins with respect to the latencies that can be observed in practical application scenarios. Theoretical derivations are verified through nontrivial simulations. [ABSTRACT FROM AUTHOR]

This article proposes an adaptive second-order sliding mode (ASOSM) controller design by means of the Lyapunov method. The notable feature of the proposed algorithm is that it only needs boundedness of the uncertainties, whereas boundedness of the derivatives of uncertainties is not demanded. Under the proposed ASOSM control scheme, the gain can be dynamically tuned, which avoids gain overestimation. The finite-time stability of the closed-loop ASOSM dynamics is proved via the Lyapunov theory. Finally, the simulation results are shown to validate the theoretical analysis. [ABSTRACT FROM AUTHOR]

In Niu and Ho (2014), an interesting issue was investigated on how an existing controller can still achieve the same control performance under the quantization case by designing the online adjusting strategy for the quantizer’s parameter. However, the above-mentioned work ignored the limitation of the coding length in the practical transmitting procedure such that the desirable performance may not be achieved due to the inevitable coding errors. Hence, this article will further consider the above-mentioned issue under the limited coding length. Different coding rules are designed for the quantized states and the adaptive quantizer’s parameters. The minimum bound of coding errors is explicitly given, which are dependent on the coding length and the coding range. Moreover, the relation between the coding length and the control performance is established, that is, the coding length has a direct effect on the convergent upper bound of the system state and the sliding domain around the specified sliding surface. Finally, an operational amplifier circuit system is provided to verify the proposed method. [ABSTRACT FROM AUTHOR]

In this article, we present a reinforcement learning-based scheme for secondary frequency control of lossy inverter-based microgrids. Compared with the existing methods in the literature, we relax the common restrictions on the system, i.e., being lossless, and the transmission lines and loads to have known constant impedances. The proposed secondary frequency control scheme does not require a priori information about system parameters and can achieve frequency synchronization within an ultimate bound in the presence of dominantly resistive and/or inductive line and load impedances, model parameter uncertainties, and time varying loads and disturbances. First, using Lyapunov theory, a feedback control is formulated based on the unknown dynamics of the microgrid. Next, a performance function is defined based on cumulative costs toward achieving convergence to the nominal frequency. The performance function is approximated by a critic neural network in real-time. An actor network is then simultaneously learning a parameterized approximation of the nonlinear dynamics and optimizing the approximated performance function obtained from the critic network. Furthermore, using the Lyapunov approach, the uniformly ultimate boundedness of the closed-loop frequency error dynamics and the networks' weight estimation errors are shown. [ABSTRACT FROM AUTHOR]

A continuous adaptive controller is developed for nonlinear dynamical systems with linearly parameterizable uncertainty involving time-varying uncertain parameters. Through a unique stability analysis strategy, a new adaptive feedforward term is developed along with specialized feedback terms, to yield an asymptotic tracking error convergence result by compensating for the time-varying nature of the uncertain parameters. A Lyapunov-based stability analysis is shown for Euler–Lagrange systems, which ensures asymptotic tracking error convergence and boundedness of the closed-loop signals. Additionally, the time-varying uncertain function approximation error is shown to converge to zero. A simulation example of a two-link manipulator is provided to demonstrate the asymptotic tracking result. [ABSTRACT FROM AUTHOR]

It is still an open problem to synthesize control with input and output quantizations for nonlinear systems subject to mismatched parametric uncertainties via backstepping design. This is because 1) the output becomes discontinuous and nondifferentiable after quantization, making the conventional recursive backstepping design method unsuitable as the differentiation of the virtual control signals does not exist, while the existing backstepping-based quantized control method is only applicable to systems modeled in normal form or systems without mismatched uncertainties; 2) it is difficult to deal with the impacts of errors caused by output quantization when the virtual control laws contain time-varying estimates of unknown parameters; and 3) since only the quantized output signal is available, the effects of certain items related to unknown parameters in currently available observers become difficult to be explicitly addressed. In this article, we present a solution to this problem by employing a dynamic filtering technique to avoid differentiating virtual control signals in backstepping design, using the parameter projection technique to design the parameter estimator and proposing a new form of state observer to facilitate the development of output feedback control. It is shown that, with the derived adaptive backstepping control involving both input and output quantizations, all the closed-loop signals are ensured bounded and the control performance in terms of the mean square error is adjustable through properly choosing certain design parameters. The benefits and effectiveness of the proposed scheme are also validated by numerical simulation. [ABSTRACT FROM AUTHOR]

This article studies the stabilization problem for switched systems in the presence of denial-of-service (DoS) attack using the event-triggered scheme. Unlike the traditional switching signal design with DoS attack, some challenges arise in the joint influence on the constraints of DoS duration/frequency, and the asynchronous behavior caused by the controller and the subsystem mode. To this end, a novel multiple Lyapunov function involving the joint effects of DoS attack and controller mode is constructed. This allows that there are no events between two consecutive switching instants. By incorporating the dwell-time switching signal with the event-triggered scheme, the considered system can be globally exponentially stabilizable when the frequency and duration of DoS attack meet certain requirements. It also shows that apart from the codesign associated with the event-triggered parameters with controller gain, the maximum allowable sampling period can be offline calculated. Moreover, the Zeno behavior is eliminated by calculating a lower bound of the event-triggered interval, over which the DoS attack is inactive. Finally, simulations are carried out to verify the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This article presents a new study on adaptive control of multi-input and multi-output (MIMO) discrete-time nonlinear systems with a noncanonical form involving parametric uncertainties. The adaptive control scheme employs a vector relative degree formulation to reconstruct the noncanonical system dynamics and derives a normal form. Then, a new matrix decomposition-based adaptive control scheme is proposed for the controlled plant with a vector relative degree $[1, 1,{\ldots }, 1]$ under some relaxed design conditions. In particular, the matrix decomposition technique is adopted to overcome the singularity problem during the adaptive estimation of an uncertain high-frequency gain matrix. The adaptive control scheme ensures closed-loop stability and asymptotic output tracking. An extension to the adaptive control of general canonical-form MIMO discrete-time nonlinear systems is also presented. Finally, through simulations, the effectiveness of the proposed control scheme is verified. [ABSTRACT FROM AUTHOR]

Although rich collection of research results on event-triggered control exist, no effort has ever been made in integrating state/output triggering and controller triggering simultaneously with backstepping control design. The primary objective of this article is, by using intermittent output signal only, to build a backstepping adaptive event-triggered feedback control for a class of uncertain nonlinear systems. To do so, we need to tackle three technical obstacles. First, the nature of the event triggering makes the transmitted output signal discontinuous, rendering the regular recursive backstepping design method inapplicable as the repetitive differentiation of virtual control signals is literally undefined. Second, the effects arisen from the event-triggering action must be properly accommodated, but the current compensating method only works for systems in normal form, thus a new method needs to be developed in order to handle nonnormal form systems. Third, as only intermittent output signal is available, and at the same time, the impacts of certain terms containing unknown parameters (arising from event triggering) need to be compensated, it is rather challenging to design a suitable state observer. To circumvent these difficulties, we employ the dynamic filtering technique to avoid the differentiation of virtual control signals in the backstepping design, construct a new compensation scheme to deal with the effects of output triggering, and build a new form of state observer to facilitate the development of output feedback control. It is shown that, with the derived adaptive backstepping output-triggered control, all the closed-loop signals are ensured bounded and the transient system performance in the mean square error sense can be adjusted by appropriately adjusting design parameters. The benefits and effectiveness of the proposed scheme are also validated by numerical simulation. [ABSTRACT FROM AUTHOR]

In this article, a set of sensors is constructed via the pinning observability approach with the help of observability criteria given in [1] and [2], in order tomake the given Boolean network (BN)be observable. Given the assumption that system states can be accessible, an efficient pinning control scheme is developed to generate an observable BN by adjusting the network structure rather than just to check system observability. Accordingly, the sensors are constructed, of which the form is consistent with that of state feedback controllers in the designed pinning control. Since this pinning control approach only utilizes node-to-node message communication instead of global state space information, the time complexity is dramatically reduced from $O(2^{2n})$ to $O(n^2+n2^d)$ , where $n\, {\text{and}}\, d$ are respectively the node number of the considered BN and the largest in-degree of vertices in its network structure. Finally, we design the sensors for the reduced D. melanogaster segmentation polarity gene network and the T-cell receptor kinetics, respectively. [ABSTRACT FROM AUTHOR]

The Battistelli–Hespanha–Mosca–Tesi (BHMT) adaptive reset switching algorithm is enhanced to admit bumpless transfer and to control a nonlinear time-varying plant using the broad class of two-degree-of-freedom nonlinear time-varying controllers. Performance, including stability and exponential stability, is proved given only that the adaptive stabilization problem is $\lambda$ -feasible, which means at every time, there exists at least one exponentially stabilizing controller. We relax two restrictive BHMT assumptions: i) the plant is linear time-invariant (LTI) over most intervals and has finite order and ii) each controller is LTI. And, we expand the scope to include a broad class of bumpless switching algorithms. An example is provided to support the improved results. [ABSTRACT FROM AUTHOR]

We consider a system of reaction–advection–diffusion partial differential equation (PDE) with a distributed input subject to an unknown and arbitrarily large time delay. Using Lyapunov technique, we derive a delay-adaptive predictor feedback controller to ensure the global stability of the closed-loop system in the $L^2$ sense. More precisely, we express the input delay as a 1-D transport PDE with a spatial argument leading to the transformation of the time delay into a spatially distributed shift. For the resulting mixed transport and reaction–advection–diffusion PDE system, we employ a PDE backstepping design and certainty equivalence principle to derive the suitable adaptive control law that compensates for the effect of the unknown time delay. Our controller ensures the global stabilization in the $L^2$ sense. Our result is the first delay-adaptive predictor feedback controller with a PDE plant subject to a delayed distributed input. The feasibility of the proposed approach is illustrated by considering a mobile robot that spread a neutralizer over a polluted surface to achieve efficient decontamination with an unknown actuator delay arising from the noncollocation of the contaminant diffusive process and the moving neutralizer source. Consistent simulation results are presented to prove the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In this article, the output feedback-based direct model reference adaptive control of piecewise affine systems and its parameter convergence are investigated. Under the slow switching assumption, it is shown that all the closed-loop signals are bounded and the output tracking error is small in the mean square sense. Built upon this result, the estimation error of controller parameters is proved to converge to a residual set if the input signal is sufficiently rich. The relationship between the size of this residual set and the switching frequency is established. Moreover, the convergence of the estimated controller parameters to their nominal values can be achieved for a certain subsystem given that this subsystem is activated for infinitely long time. Simulation results validate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

We approach the problem of stabilizing a dynamical system while optimizing a cost and satisfying safety constraints and control limitations. For (nonlinear) affine control systems and quadratic costs, it has been shown that control barrier functions (CBFs) guaranteeing safety and control Lyapunov functions (CLFs) enforcing convergence can be used to (conservatively) reduce the optimal control problem to a sequence of quadratic programs (QPs). Existing works in this category have two main limitations. First, with one exception, they are based on the assumption that the relative degree of the system with respect to a function enforcing a safety constraint is one. Second, the QPs can easily become infeasible, in particular for problems with many safety constraints and tight control limitations. We propose high-order CBFs (HOCBFs), which can accommodate systems of arbitrary relative degrees. For each safety constraint, by using Lyapunov-like conditions, we construct a set of controls that renders the intersection of a set of sets forward invariant, which implies the satisfaction of the original constraint. We formulate optimal control problems with constraints given by HOCBF and CLF, and propose two methods—the penalty method and the parameterization method—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 adaptive cruise control and robot control problems. [ABSTRACT FROM AUTHOR]

In this article, we investigate the problem of practical output regulation, i.e., to design a controller that brings the system output in the vicinity of a desired target value while keeping the other variables bounded. We consider uncertain systems that are possibly nonlinear and the uncertainty of their linear parts is modeled element wise through a parametric family of matrix boxes. An optimization-based design procedure is proposed that delivers a continuous-time control and estimates the maximal regulation error. We also analyze an event-triggered emulation of this controller, which can be implemented on a digital platform, along with an explicit estimate of the regulation error. [ABSTRACT FROM AUTHOR]

In biology networks, social networks, mobile robots, and many real networks, spatial factors are crucial to the evolution of networks and individual interactions are not always continuous. In this article, a kind of intermittently coupled spatiotemporal networks (ICSNs) is proposed, where the couplings among nodes are intermittent and the coupling strengths are related to both time and space. By constructing piecewise auxiliary functions and developing a direct error method, a distributed intermittent adaptive protocol and its pinning form are designed to determine the space-time dependent weights of edges to realize synchronization of ICSNs. Lastly, the theoretical analysis is supported by means of a numerical example. [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]

In this article, we investigate the robust stabilization of linear time-invariant (LTI) systems with external disturbances via event-triggered impulsive control (ETIC). Especially, in order to suppress the disturbances effectively, the impulsive instant sequence is generated through the sliding-variable-based event-triggering mechanism (ETM). Based on the proposed ETM, some sufficient conditions are derived to ensure the robust stabilization of the LTI systems and to exclude Zeno phenomenon. It is shown that the system states are ultimately bounded under the ETIC, and the ultimate bound can be arbitrarily small by selecting the appropriate parameter of ETM. More interestingly, it is proved that our obtained results can well deal with the case of unknown bounded external disturbances, which is often addressed by the adaptive control in the previous results. Then, the theoretical results are applied to the motor servo systems in the presence of external disturbances. Finally, two illustrative examples are presented to show the validity of the results. [ABSTRACT FROM AUTHOR]

Comparing with traditional stochastic differential equations involving white noise, random differential equations (RDEs) with colored noise are claimed to have more practical meaning. This article considers the event-triggered adaptive tracking control for RDE systems with coexisting parametric uncertainties and severe nonlinearities. Combining a tracking error-based dynamic gain with a relative threshold event triggered control mechanism, the tracking control problem for the random systems is solved without Zeno behavior. The tracking error can be rendered small enough by tuning design parameters. First, a series of adaptive control laws are designed by using backstepping technique. Then, two special cases are considered and the main results are extended to MIMO systems. Finally, a simulation example confirms the validity of the results. To the best of the authors’ knowledge, this article serves as the first attempt of event-based control for RDE systems. [ABSTRACT FROM AUTHOR]

In this article, a robust nonlinear model reference adaptive control (MRAC) is proposed for disturbed linear systems, i.e., linear systems with parameter uncertainties, and external time-dependent perturbations or nonlinear unmodeled dynamics matched with the control input. The proposed nonlinear control law is composed of two nonlinear adaptive gains. Such adaptive gains allow the control to counteract the effects of some perturbations and nonlinear unmodeled dynamics ensuring asymptotic convergence of the tracking error to zero, and the boundedness of the adaptive gains. The nonlinear controller synthesis is given by a constructive method based on the solution of linear matrix inequalities. Besides, the simulation results show that, due to the nonlinearities, the rate of convergence of the proposed algorithm is faster than that provided by a classic MRAC. [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]

A robust adaptive control allocation algorithm with actuator failure compensation is presented in this article for a class of cascade ODE-string systems depicted by ordinary differential equations (ODEs) and partial differential equations. The proposed control scheme including actuator fault compensation and allocation algorithm uniformly stabilizes the cascade ODE-string system in the presence of actuator faults, parameter uncertainties and environmental perturbations, and effectively reduces the controller complexity by adaptively grouping redundant actuators. Since this control method needs full-state measurement of the ODE system, it can be regarded as a state-feedback control instead of an output-feedback control. Control design and proof of the closed-loop system stability are implemented by Lyapunov’s direct method. Numerical simulations are finally analyzed to illustrate the feasibility of the proposed control scheme. [ABSTRACT FROM AUTHOR]

For a multiple-input–multiple-output (MIMO) nonlinear feedback system, the robustness against uncertain time-variation (slow or infrequently large) in the feedback loop is investigated in an input–output framework. A couple of sufficient conditions in terms of bounds on average rates of time-variation for the system to be stable are derived. The conditions provide a useful tool for designing adaptive controllers for systems against uncertain large time-variation. [ABSTRACT FROM AUTHOR]

This work develops two kinds of adaptive state feedback shared-control algorithms for a class of nonlinear mechanical systems in the presence of output constraints described by a set of linear inequalities. The parametric uncertainties and unknown external disturbances in the dynamical model are compensated by the proposed adaptive control laws for the feedback controller. In particular, an adaptive fixed-time state-feedback control law is also developed after the classical robust adaptive state-feedback control law design. The properties of the closed-loop shared-control systems are studied by using Lyapunov method. Simulation results demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

A discrete-time adaptive control approach for uncertain linear multivariable networked systems is proposed. It is capable of dealing with unknown time delays introduced by a communication network between a plant and a controller. Based on the idea of model reference adaptive control, two adaptive laws are presented to reduce the conservativeness that is usually introduced when the time delays are unknown. The stability of the closed-loop system is proven. Simulation examples provide a comparison of the proposed techniques to a nonadaptive algorithm. [ABSTRACT FROM AUTHOR]

Multiagent distributed optimal coordination (DOC) involves the motion conflicts of a large numbers of physical systems, which lead to significant safety challenges in terms of collision avoidance. This article studies the problem of secure DOC for multiple uncertain Euler–Lagrangian (EL) systems. The objective is to steer each EL agent to achieve the optimization task while avoiding collisions with other agents. The main challenge focuses on the co-design of optimal coordination strategy and collision avoidance mechanism. The safety barrier certificates in the closed form of path integrals are constructed, which generate provably collisions-free behaviors. With convex optimization and adaptive nonlinear control, a fully distributed protocol is proposed. Based on Lyapunov method and boundedness analysis for the barrier functions, it is proved that the protocol simultaneously guarantees the global convergence and collision avoidance of the EL systems in the presence of parametric uncertainties. [ABSTRACT FROM AUTHOR]

In this article, we consider the problem of tracking for a discrete-time plant with unknown plant parameters; we assume knowledge of an upper bound on the plant order, and for each admissible order we assume knowledge of a compact set in which the plant parameters lie. We carry out parameter estimation of an associated auxiliary model; indeed, for each admissible dimension, we cover the set of admissible parameters by a finite number of compact and convex sets and use an original-projection-algorithm-based estimator for each set. At each point in time, we employ a switching algorithm to determine which model and parameter estimates are used in the pole-placement-based control law. We prove that this adaptive controller guarantees desirable linear-like closed-loop behavior: exponential stability, a bounded noise gain in every $p$ -norm, a convolution bound on the effect of the exogenous inputs, as well as exponential tracking for certain classes of reference and noise signals; this linear-like behavior is leveraged to immediately show tolerance to a degree of plant time-variations and unmodeled dynamics. [ABSTRACT FROM AUTHOR]

This article introduces a new class of nonsmooth extremum seeking controllers (ESCs) with convergence bounds given by class- $\mathcal {K}\mathcal {L}$ functions that have a uniformly bounded settling time. These ESCs are characterized by nominal average systems that render uniformly globally fixed-time stable (UGFxTS), the set of minimizers of the response map of a stable nonlinear plant. Given that, under suitable tuning of the parameters of the controllers, the ESCs inherit the convergence properties of their average systems, the proposed dynamics can achieve a better transient performance compared to the traditional ESCs based on gradient descent or Newton flows. Moreover, for the case when the plant is a static map, the convergence time of the proposed algorithms can be prescribed a priori by the users for all initial conditions without the need of retuning the gain of the learning dynamics of the ESC. Since autonomous feedback controllers with fixed-time convergence properties are necessarily non-Lipschitz continuous, standard averaging and singular perturbation tools, traditionally used in ESC, are not applicable anymore. We address this issue by using averaging and singular perturbation tools for nonsmooth and set-valued systems, which further allows us to consider ESCs modeled by discontinuous vector fields that are typical in fixed-time and finite-time optimization problems. [ABSTRACT FROM AUTHOR]

This article studies the distributed entrapping control problem of multiple mobile agents based on bearing and velocity measurements. A time-varying entrapping formation with a prescribed shape, which is elastic and rotational with respect to the target is adopted. Such a formation allows agents to move even in restricted areas while still entrapping the target as a whole. To achieve the entrapping formation based on bearing measurements, a leader-follower structure is adopted, and a design framework integrating formation shape observers, relative position estimators, and distributed controllers is proposed. The rigorous stability analysis of the overall system is also given. It is shown that the stability of the closed loop system is guaranteed if its bearing observability is satisfied. Since the desired formation is determined by the trajectories of the leaders, we characterize the sufficient conditions on the trajectories of the leaders such that the bearing observability of the closed loop system is always satisfied, and the estimation errors and the formation tracking errors converge to zero asymptotically. Simulations verify the effectiveness of the proposed framework. [ABSTRACT FROM AUTHOR]

This article addresses the problem of cooperative adaptive containment control for multiagent systems, which specifies the objective of jointly achieving containment control and accurate adaptive learning/identification of unknown system parameters. We consider a class of linear uncertain multiagent systems with multiple leaders subject to bounded unmeasurable inputs and multiple followers subject to unknown system dynamics. A novel cooperative adaptive containment control architecture is proposed, which consists of a discontinuous nonlinear state-feedback control law and a filter-based cooperative adaptation law. This new control architecture is compelling in the sense that exponential convergence of both containment tracking errors to zero and adaptation parameters to their true values can be achieved simultaneously under a mild cooperative finite-time excitation condition. This condition significantly relaxes existing ones (e.g., persistent excitation and finite-time excitation) for parameter identification in adaptive control systems. Effectiveness of the proposed approach has been demonstrated through both rigorous analysis and a case study. [ABSTRACT FROM AUTHOR]

An output robust adaptive control is designed for a class of Lipschitz nonlinear systems under assumption that the measurements are available with a constant bias and the state equations linearly parameterized by unknown parameters and external disturbances. A dynamic state reconstruction (synthesis of an observer) is avoided by using delayed values of the output in the feedback and adaptation laws. The analysis of robust stability for the resulted time-delay system is performed by using the Lyapunov–Krasovskii approach. The control and adaptation gains can be selected as a solution of the proposed linear matrix inequalities. This research is motivated by a nonlinear pendulum control problem, and the efficacy of the developed control is demonstrated on this application through experiments. [ABSTRACT FROM AUTHOR]

In this article, an adaptive consensus tracking control scheme is proposed for a class of high-order nonlinear multiagent systems with unknown control directions. Different from the existing results, the unknown control directions are not required to be identical and also unknown time-varying actuator faults are taken into account simultaneously. We design some novel Nussbaum functions and construct a monotonously increasing sequence in which the effects of our multiple Nussbaum functions reinforce rather than counteract each other. Moreover, some integrable auxiliary signals and a novel contradiction argument are introduced in the design and analysis. With these efforts, the obstacle jointly caused by the unknown control directions and actuator faults are circumvented, and the global stability of the overall closed-loop system and asymptotic convergence to zero of tracking errors are successfully achieved. Simulation results illustrate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

This article studies model reference adaptive control (MRAC) for a class of stochastic discrete time control systems with time delays in the control input. In particular, a unified fully probabilistic control framework is established to develop the solution to the MRAC, where the controller is the minimizer of the Kullback–Leibler divergence between the actual and desired joint probability density functions of the tracking error and the controller. The developed framework is quite general, where all the components within this framework, including the controller and system tracking error, are modeled using probabilistic models. The general solution for arbitrary probabilistic models of the framework components is first obtained and then demonstrated on a class of linear Gaussian systems with time delay in the main control input, thus obtaining the desired results. The contribution of this article is twofold. First, we develop a fully probabilistic design framework for MRAC, referred to as model reference fully probabilistic design, for stochastic dynamical systems. Second, we establish a systematic pedagogic procedure that is based on deriving explicit forms for the required predictive distributions for obtaining the causal form of the randomized controller when input delays are present. [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]

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. [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]

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]

In this article, we present a distributed robust adaptive gradient controller for distance-based formation systems with exogenous disturbances. Based on the proposed controller, we consider two undirected formation topologies: Minimally infinitesimally rigid formation and nonminimally infinitesimally rigid formation. For both formation systems, we show that the distributed robust adaptive gradient controller guarantees a local stability of formation systems with exogenous disturbances. Furthermore, an upper-boundedness set of squared-distance error is obtained based on Lyapunov stability analysis for minimally infinitesimally rigid formation systems. We verify the validity of the theoretical results through numerical simulations. [ABSTRACT FROM AUTHOR]

This article investigates the adaptive control problem for systems with time-varying parameters using the so-called congelation of variables method. First, two scalar examples to illustrate how to deal with time-varying parameters in the feedback path and in the input path, respectively, are discussed. The control problem for an n-dimensional lower triangular system via state feedback is then discussed to show how to combine the congelation of variables method with adaptive backstepping techniques. To achieve output regulation problem via output feedback, problem which cannot be solved directly due to the coupling between the input and the time-varying perturbation, the ISS of the inverse dynamics, referred to as strong minimum-phaseness, is exploited. This allows converting such coupling into the coupling between the output and the time-varying perturbation. A set of filters, resulting in ISS state estimation error dynamics, are designed to cope with the unmeasured state variables. Finally, a controller is designed based on a small-gain-like analysis that takes all subsystems into account. Simulation results show that the proposed controller achieves asymptotic output regulation and outperforms the classical adaptive controller, in the presence of time-varying parameters that are neither known nor asymptotically constant. [ABSTRACT FROM AUTHOR]

In this article, we propose a novel family of Lie algebra valued functions FR on special orthogonal group SO(3). Each function belonging to this family induces a novel controller that stabilizes a rigid body attitude. All controllers induced by the family FR form a controller class CR. This novel controller class CR contains both local and almost-global asymptotically stable controllers, and this article presents geometric stability results of the whole controller class CR. [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]