Boris M. Mirkin

Decentralized output-feedback MRAC of linear state delay systems

In this note, we develop coordinated decentralized output-feedback adaptive controllers for a class of large-scale systems with state time delays in the subsystems and in the interconnections. We present a decentralized model reference adaptive control scheme which requires an exchange of signals between the different reference models, but does not involve the exchange of output signals between the different subsystems. It can not only guarantee closed-loop stability but also asymptotic zero tracking errors when uncertainties and delays are present in the subsystems and interconnections. Closed-loop signal boundedness and asymptotic output-feedback tracking are proven analytically and verified by simulation.

Model reference adaptive control of state delayed system with actuator failures

This paper develops adaptive state feedback control schemes for a class of linear systems with state delay in the presence of unknown actuator failures. The main contributions of this paper are the development of two controller parametrizations which attempt to anticipate the future states, the introduction of an appropriate Lyapunov–Krasovskii type functional to design the new class of adaptation algorithms, and a stability proof.

Robust Adaptive Output-Feedback Tracking for a Class of Nonlinear Time-Delayed Plants

Within the model reference adaptive control (MRAC) framework, a continuous adaptive output-feedback control scheme is developed for a class of nonlinear SISO dynamic systems with time delays which is robust with respect to unknown time-varying plant delays and to an external disturbance with unknown bounds. A special form of the Lyapunov-Krasovskii functional with a “virtual” adaptation gain vector is introduced to prove stability.

Output feedback model reference adaptive control for multi-input–multi-output plants with state delay

Two new output feedback adaptive control schemes based on Model Reference Adaptive Control (MRAC) and adaptive laws for updating the controller parameters are developed for a class of linear multi-input–multi-output (MIMO) systems with state delay. An effective controller structure established on a new error equation parametrization is proposed to achieve tracking with the error tending to zero asymptotically. To achieve exact asymptotical tracking, we introduce, in the standard MRAC structure for plants without delay, a new additional adaptive feedforward control component as an output of a dynamical system driven by the reference signal. Adaptive laws are developed using the SPR-Lyapunov design approach and two assumptions regarding the prior knowledge of the high-frequency matrix Kp. This work is the first asymptotic exact zero tracking results for this class of systems in the framework of the certainty equivalence approach.

Output-Feedback Model Reference Adaptive Control for Continuous State Delay Systems

This paper develops a new approach for the output model reference adaptive control of linear continuous-time plants with state delays. The main idea is to include into the control law a feedforward component that compensates for the delayed states, in addition to output feedback. The feedforward is formed by special adaptively adjusted prefilters as a function of the delayed state of the reference model. The output feedback component is designed as for a plant without delay, but applied to the time-delay plant. Such a controller structure containing adaptive output feedback and adaptive prefilters from the delayed reference model makes it possible to solve the problem of adaptive exact asymptotic output tracking under parametric uncertainties. The stability is analyzed using the Lyapunov-Krasovskii functional method. A simulated example illustrates the new controller.

Adaptive output-feedback tracking: The case of MIMO plants with unknown, time-varying state delay

In this paper, we develop a simple model reference adaptive control (MRAC) scheme for a class of multi-input-multi-output (MIMO) linear dynamic systems with unknown state delay which is also robust with respect to an external disturbance with unknown bound. A suitable Lyapunov–Krasovskii type functional with “virtual” gain is introduced to design the adaptation algorithms and to prove stability.

Robust Output-Feedback Model Reference Adaptive Control of SISO Plants With Multiple Uncertain, Time-Varying State Delays

Within the model reference adaptive control framework, a simple adaptive output-feedback control scheme is developed for a class of linear single-input single-output dynamic systems with multiple state delays which is robust with respect to multiple unknown time-varying plant delays and to an external disturbance with unknown bounds. A special form of the Lyapunov-Krasovskii functional with ldquovirtualrdquo adaptation gain is introduced to prove stability.

Asymptotic sliding mode control approach to adaptive distributed tracking problem for multi-agent nonlinear delayed systems

In this article, a sliding mode coordinated decentralised state-feedback model reference adaptive control is developed for a class of large-scale uncertain multi-agent systems with time-varying delays in the nonlinear interconnections. The design procedure is based on a combination of the model coordination concept and a sliding mode control methodology. Novel decentralised controller parameterisations that are robust to unknown information exchange delays and to external disturbances with unknown bounds are proposed. Two different controllers are designed: one with discontinuous and one with continuous control action, respectively.

Coordinated decentralized sliding mode MRAC with control cost optimization for a class of nonlinear systems

In this paper, we develop an approach for solving the problem of sliding mode decentralized adaptive state-feedback tracking with continuous control actions for a class of uncertain nonlinear dynamical systems. In addition to the traditional asymptotic zero error tracking specification in the sliding mode decentralized model reference adaptive control (MRAC) problem formulation, here an additional requirement is specified explicitly in the problem statement. The tracking objective is described by a set of admissible reference trajectories, called a performance tube. The input signal to the reference model, selected within specified bounds, is used as a design parameter. The best reference trajectory is found by solving an additional optimization problem whose criterion penalizes the variance of the control signal.

Continuous model reference adaptive control with sliding mode for a class of nonlinear plants with unknown state delay

In this paper, we develop a model reference adaptive control (MRAC) scheme with sliding mode for a class of nonlinear dynamic systems with state delay which is robust with respect to an unknown plant delay, to a nonlinear perturbation, and to an external disturbance with unknown bounds. A novel Lyapunov-Krasovskii type functional is introduced to design the adaptive controller with smooth control action, and the stability proof.