Adaptive Output Feedback Control Law Research Articles

Event-triggered robust cooperative output regulation for a class of linear multi-agent systems with an unknown exosystem

This paper investigates the robust cooperative output regulation problem for a class of heterogeneous uncertain linear multi-agent systems with an unknown exosystem via event-triggered control (ETC). By utilizing the internal model approach and the adaptive control technique, a distributed adaptive internal model is constructed for each agent. Then, based on this internal model, a fully distributed ETC strategy composed of a distributed event-triggered adaptive output feedback control law and a distributed dynamic event-triggering mechanism is proposed, in which each agent updates its control input at its own triggering time instants. It is shown that under the proposed ETC strategy, the robust cooperative output regulation problem can be solved without requiring either the global information associated with the communication topology or the bounds of the uncertain or unknown parameters in each agent and the exosystem. A numerical example is provided to illustrate the effectiveness of the proposed control strategy.

Event-Sampled Adaptive Neural Course Keeping Control for USVs Using Intermittent Course Data

This paper addresses the issue of course keeping control (CKC) for unmanned surface vehicles (USVs) under network environments, where various challenges, such as network resource constraints and discontinuities of course and yaw caused by data transmission, are taken into account. To tackle the issue of network resource constraints, an event-sampled scheme is developed to obtain the course data, and a novel event-sampled adaptive neural-network-based state observer (NN–SO) is developed to achieve the state reconstruction of discontinuous yaw. Using a backstepping design method, an event-sampled mechanism, and an adaptive NN–SO, an adaptive neural output feedback (ANOF) control law is designed, where the dynamic surface control technique is introduced to solve the design issue caused by the intermission course data. Moreover, an event-triggered mechanism (ETM) is established in a controller–actuator (C–A) channel and a dual-channel event-triggered adaptive neural output feedback control (ETANOFC) solution is proposed. The theoretical results show that all signals in the closed-loop control system (CLCS) are bounded. The effectiveness is verified through numerical simulations.

Adaptive Output Feedback Control for Constrained Switched Systems with Input Quantization

This paper investigates adaptive output feedback control problem for switched uncertain nonlinear systems with input quantization, unmeasured system states and state constraints. Firstly, fuzzy logic systems are introduced to identify system uncertainties, then the fuzzy based observer is constructed to estimate unavailable states. Secondly, combing the backstepping technique and the barrier Lyapunov function method, an adaptive fuzzy output feedback control law is designed, which guarantees that all signals in the closed-loop system are bounded, the system output tracks the reference signal, and system states satisfy their corresponding constraint conditions. Finally, simulation results further show the good performances of the proposed control scheme.

Adaptive output feedback controller of resisting large measurement noises for MIMO nonlinear systems

In this paper, we propose an adaptive output feedback control law for MIMO nonlinear systems with distinct unknown measurement errors in each output. The nonlinear terms have incremental rates which include nonlinear functions of output and polynomials of output multiplying unknown constants. By introducing an observer, and two classes of particular dual adaptive high-gains and a class of exclusive constant high-gains, an output feedback controller is developed to stabilise the MIMO nonlinear system. The designed controller is able to tolerate uncertain measurement errors with a relatively wide range. Finally, some simulations are provided to corroborate the theoretical analysis.

Adaptive Neural Output Feedback Tracking Control of Underactuated Ships Against Uncertainties in Kinematics and System Matrices

Adaptive neural output feedback tracking control is developed for underactuated ships with uncertainties in kinematics (i.e., kinematic uncertainties) and uncertain off-diagonal terms in the matrices of their system dynamics (i.e., dynamic uncertainties), where radial basis function networks are incorporated. As the kinematic uncertainties unavoidably exist in the off-diagonal terms of system matrices and only the posture information (position variables and yaw angle) of the ship is available, the velocities should be observed and the kinematic and dynamic uncertainties should be simultaneously compensated to achieve the satisfactory ship tracking control performance. Therefore, the kinematic and dynamic uncertainties of the underactuated ship are rigorously derived. The kinematic equations with uncertainties are then derived such that the proposed nonlinear velocity observer can be used to estimate the combined velocities and kinematic uncertainties using the posture information irrespective of the ship dynamics. The dynamic uncertainties are also derived while taking into consideration the uncertainties in the system matrices. An adaptive neural uncertainty observer is then proposed to estimate the dynamic uncertainties. In this way, the proposed adaptive neural output feedback control law can compensate for the uncertainties in both the kinematics and dynamics. The estimation errors in the combined velocities and kinematic uncertainties and the dynamic uncertainties are rigorously considered in the proposed controller design. A stability analysis and the simulation results of the ship tracking control system are provided to demonstrate the validity of the proposed method.

Adaptive distributed observer design for containment control of heterogeneous discrete-time swarm systems

This paper develops both adaptive distributed dynamic state feedback control law and adaptive distributed measurement output feedback control law for heterogeneous discrete-time swarm systems with multiple leaders. The convex hull formed by the leaders and the system matrix of leaders is estimated via an adaptive distributed containment observer. Such estimations will feed the followers so that every follower can update the system matrix of the corresponding adaptive distributed containment observer and the system state of their neighbors. The followers cooperate with each other to achieve leader–follower consensus and thus solve the containment control problem over the network. Numerical results demonstrate the effectiveness and computational feasibility of the proposed control laws.

Event-Triggered Robust Output Regulation of Uncertain Linear Systems With Unknown Exosystems

This article studies the robust output regulation problem (RORP) for a class of uncertain linear systems with unknown exosystems via event-triggered control (ETC). Compared with existing related works, the system matrix of the exosystem under consideration is allowed to contain unknown parameters. Based on an adaptive internal model, an ETC strategy composed of an event-triggered adaptive output feedback control law and an output-based event-triggering mechanism is proposed such that the RORP is solved. It is shown that under the proposed ETC strategy, the tracking error converges to zero asymptotically in spite of the unknown exosystem, and meanwhile the occurrence of Zeno behavior is prevented. Finally, two examples are provided to illustrate the effectiveness of the proposed control strategy.

Traffic congestion control for Aw–Rascle–Zhang model

This paper develops boundary feedback control laws to reduce stop-and-go oscillations in congested traffic. The macroscopic traffic dynamics are governed by Aw–Rascle–Zhang (ARZ) model, consisting of second-order nonlinear partial differential equations (PDEs). A criterion to distinguish free and congested regimes for the ARZ traffic model leads to the study of hetero-directional hyperbolic PDE model of congested traffic regime. To stabilize the oscillations of traffic density and speed in a freeway segment, a boundary input through ramp metering is considered. We discuss the stabilization problem for freeway segments respectively, upstream and downstream of the ramp. For the more challenging upstream control problem, our full-state feedback control law employs a backstepping transformation. Both collocated and anti-collocated boundary observers are designed. The exponential stability in L2 sense and finite time convergence to equilibrium are achieved and validated with simulation. In the absence of relaxation time and boundary parameters’ knowledge, we propose adaptive output feedback control design. Control is applied at outlet and the measurement is taken from inlet of the freeway segment. We use the backstepping method to obtain an observer canonical form in which unknown parameters multiply with measured output. A parametric model based on this form is derived and gradient-based parameter estimators are designed. An explicit state observer involving the delayed values of the input and the output is introduced for state estimation. Using the parameter and state estimates, we develop an adaptive output feedback control law which achieves convergence to the steady regulation in the L2 sense.

Multiple Model Adaptive Attitude Control of LEO Satellite with Angular Velocity Constraints

In this paper, the multiple model adaptive control is utilized to improve the transient response of attitude control system for a rigid spacecraft. An adaptive output feedback control law is proposed for attitude control under angular velocity constraints and its almost global asymptotic stability is proved. The multiple model adaptive control approach is employed to counteract large uncertainty in parameter space of the inertia matrix. The nonlinear dynamics of a low earth orbit satellite is simulated and the proposed control algorithm is implemented. The reported results show the effectiveness of the suggested scheme.

Universal adaptive regulation for a class of nonlinear systems with unknown time delays and output function via output feedback

This paper investigates the adaptive output feedback control problem for a class of nonlinear systems with unknown time delays and output function. The system satisfies linear growth condition with an unknown growth rate. First of all, based on a dynamic gain scaling technique, we present a new dynamic high-gain observer without requiring precise information of the output function. Then, by employing the idea of universal control and the backstepping method, a universal adaptive output feedback control law is designed to globally regulate all the states of the system. A simulation example is presented to illustrate the effectiveness of the proposed design scheme.

Adaptive Rejection of Unmatched General Periodic Disturbances by Dynamic Output Feedback

The paper considers rejection of unmatched general periodic disturbances with time-varying gains for a class of nonlinear systems. The period of the periodic disturbances is known, the gains of the disturbances depend on the output of the system, and the coefficient vector of the disturbance input channel is not assumed to be a Hurwitz vector. A novel filtered transformation is presented. Based on the filtered transformation, an adaptive output feedback control law is proposed, which guarantees that the output of the closed loop system converges to zero.

Modeling and Automatic Feedback Control of Tremor: Adaptive Estimation of Deep Brain Stimulation

This paper discusses modeling and automatic feedback control of (postural and rest) tremor for adaptive-control-methodology-based estimation of deep brain stimulation (DBS) parameters. The simplest linear oscillator-based tremor model, between stimulation amplitude and tremor, is investigated by utilizing input-output knowledge. Further, a nonlinear generalization of the oscillator-based tremor model, useful for derivation of a control strategy involving incorporation of parametric-bound knowledge, is provided. Using the Lyapunov method, a robust adaptive output feedback control law, based on measurement of the tremor signal from the fingers of a patient, is formulated to estimate the stimulation amplitude required to control the tremor. By means of the proposed control strategy, an algorithm is developed for estimation of DBS parameters such as amplitude, frequency and pulse width, which provides a framework for development of an automatic clinical device for control of motor symptoms. The DBS parameter estimation results for the proposed control scheme are verified through numerical simulations.

Nonlinear adaptive control of an underwater towed vehicle

This paper addresses the problem of simultaneous depth tracking and attitude control of an underwater towed vehicle. The system proposed uses a two-stage towing arrangement that includes a long primary cable, a gravitic depressor, and a secondary cable. The towfish motion induced by wave driven disturbances in both the vertical and horizontal planes is described using an empirical model of the depressor motion and a spring-damper model of the secondary cable. A nonlinear, Lyapunov-based, adaptive output feedback control law is designed and shown to regulate pitch, yaw, and depth tracking errors to zero. The controller is designed to operate in the presence of plant parameter uncertainty. When subjected to bounded external disturbances, the tracking errors converge to a neighbourhood of the origin that can be made arbitrarily small. In the implementation proposed, a nonlinear observer is used to estimate the linear velocities used by the controller thus dispensing with the need for costly sensor suites. The results obtained with computer simulations show that the controlled system exhibits good performance about different operating conditions when subjected to sea-wave driven disturbances and in the presence of sensor noise. The system holds promise for application in oceanographic missions that require depth tracking or bottom-following combined with precise vehicle attitude control.

Adaptive output-feedback control for a class of uncertain stochastic non-linear systems with time delays

In this paper, we investigate the adaptive output-feedback stabilisation for a class of stochastic non-linear systems with time-varying time delays. First, we give some sufficient conditions to ensure the existence and uniqueness of the solution process for stochastic non-linear systems with time delays, and introduce a new stability notion and the related criterion. Then, for a class of stochastic non-linear systems with time-varying time delays, uncertain parameters in both drift and diffusion terms, and general constant virtual control coefficients, we present a systematic design procedure for a memoryless adaptive output-feedback control law by using the backstepping method. It is shown that under the control law based on a memoryless observer, the closed-loop equilibrium of interest is globally stable in probability, and moreover, the solution process can be regulated to the origin almost surely.

Adaptive output feedback stabilization of a class of uncertain continuous stirred tank reactors

The problem of global temperature control for a general class of chemical reactors is addressed and solved using Lyapunov techniques. The main results of the paper show that, under reasonable and easy to test assumptions, global temperature control can be achieved with a bounded output feedback control law and with an adaptive output feedback control law. The control bounds can be very general and tight, and the only condition to be fulfilled is a simple and natural feasibility condition, namely that the steady state control is admissible. The theory is illustrated on a simple simulation example.

Topological Aspects of Universal Adaptive Stabilization

In this paper we consider two problems in “non–identifier-based,” universal adaptive control within the framework of Mårtensson [Adaptive Stabilization, Ph.D. thesis, Lund Institute of Technology, 1986]. In this framework, any linear system stabilizable by constant linear output feedback is adaptively stabilized by an adaptive piecewise-linear output feedback control law. The essential feature we exploit is that of a piecewise-linear output feedback which switches through a set of feedback matrices, with switching controlled by an output-driven differential equation. For each initial condition the state of the system converges to zero and the time-varying gain matrix converges to a “limit gain.” In this setting we consider two related problems. The first concerns the sensitivity of closed-loop solutions under small perturbations of the initial data. The second concerns generic properties, with respect to the set of initial conditions, of stabilization by the limit gain. We adopt a topological approach, based on a decomposition of the dynamics of the resultant nonlinear, closed-loop system into a sequence of homeo/diffeomorphisms derived from the switching nature of the dynamics. Using this decomposition we show that the set of initial conditions for which solutions are stable under small perturbations and the limiting gain is stabilizing has full Lebesgue measure and dense interior. This latter result has been conjectured in the literature. The results are illustrated by examples of planar control systems where the sets of initial conditions yielding nonstabilizing limit gains are computed.