Discrete-time combined model reference adaptive control

The discrete-time version of continuous-time combined model reference adaptive control (CMRAC) is presented in this paper. A global stability proof of the overall adaptive scheme is given using arguments similar to those used in discrete-time direct model reference adaptive control (DMRAC) but properly modified to account for the different structure of CMRAC with respect to DMRAC. © 1997 by John Wiley & Sons, Ltd.     

Lyapunov‐stable discrete‐time model reference adaptive control

Discrete‐time model reference adaptive control (MRAC) is considered with both least squares and projection algorithm parameter identification. For both cases complete Lyapunov proofs are given for stability and convergence. The results extend the approach of Johansson (Int. J. Control 1989; 50 (3):859–869) to include Lyapunov stability for MRAC when the normalized projection algorithm is used for parameter identification. Copyright © 2005 John Wiley & Sons, Ltd.     

A new model reference adaptive control for linear time‐varying systems

Recent results on the adaptive control of linear time‐varying systems have considered mostly the case in which the range or rate of parameter variations is small. In this paper, a new state feed‐back model reference adaptive control is developed for systems with bounded arbitrary parameter variations. The important feature of the proposed adaptive control is an uncertainty estimation algorithm, which guarantees almost zero tracking error. Note that the conventional parameter estimation algorithm in the adaptive control guarantees only bounded tracking error. Copyright © 2000 John Wiley & Sons, Ltd.     

Model reference adaptive iterative learning control for linear systems

In this paper, we propose a model reference adaptive control (MRAC) strategy for continuous‐time single‐input single‐output (SISO) linear time‐invariant (LTI) systems with unknown parameters, performing repetitive tasks. This is achieved through the introduction of a discrete‐type parametric adaptation law in the ‘iteration domain’, which is directly obtained from the continuous‐time parametric adaptation law used in standard MRAC schemes. In fact, at the first iteration, we apply a standard MRAC to the system under consideration, while for the subsequent iterations, the parameters are appropriately updated along the iteration‐axis, in order to enhance the tracking performance from iteration to iteration. This approach is referred to as the model reference adaptive iterative learning control (MRAILC). In the case of systems with relative degree one, we obtain a pointwise convergence of the tracking error to zero, over the whole finite time interval, when the number of iterations tends to infinity. In the general case, i.e. systems with arbitrary relative degree, we show that the tracking error converges to a prescribed small domain around zero, over the whole finite time interval, when the number of iterations tends to infinity. It is worth noting that this approach allows: (1) to extend existing MRAC schemes, in a straightforward manner, to repetitive systems; (2) to avoid the use of the output time derivatives, which are generally required in traditional iterative learning control (ILC) strategies dealing with systems with high relative degree; (3) to handle systems with multiple tracking objectives (i.e. the desired trajectory can be iteration‐varying). Finally, simulation results are carried out to support the theoretical development. Copyright © 2006 John Wiley & Sons, Ltd.     

Immersion and invariance adaptive control for discrete‐time systems in strict‐feedback form with input delay and disturbances

This work presents a new adaptive control algorithm for a class of discrete‐time systems in strict‐feedback form with input delay and disturbances. The immersion and invariance formulation is used to estimate the disturbances and to compensate the effect of the input delay, resulting in a recursive control law. The stability of the closed‐loop system is studied using Lyapunov functions, and guidelines for tuning the controller parameters are presented. An explicit expression of the control law in the case of multiple simultaneous disturbances is provided for the tracking problem of a pneumatic drive. The effectiveness of the control algorithm is demonstrated with numerical simulations considering disturbances and input‐delay representative of the application.     

Indirect model reference adaptive control with dynamic adjustment of parameters

The paper discusses in detail a new method for indirect model reference adaptive control (MRAC) of linear time-invariant continuous-time plants with unknown parameters. The method involves not only dynamic adjustment of plant parameter estimates but also those of the controller parameters. Hence the overall system can be described by a set of non-linear differential equations as in the case of direct control. Many of the difficulties encountered in the conventional indirect approach, where an algebraic equation is solved to determine the control parameters, are consequently bypassed in this method. The proof of stability of the equilibrium state of the overall system is found to be different from that used in direct control. Using Lyapunov's theory, it is first shown that the parameter errors between the parameter estimates of the identifier and the true parameters of the plant, as well as those between the actual parameters of the controller and their desired values, are bounded. Following this, using growth rates of signals in the adaptive loop as well as order arguments, it is shown that the error equations are globally uniformly stable and that the tracking (control) error tends to zero asymptotically. This in turn establishes the fact that both direct and indirect model reference adaptive schemes require the same amount of prior information to achieve stable adaptive control.     

Reinforcement learning based closed-loop reference model adaptive flight control system design

In this study, we present a reinforcement learning (RL)-based flight control system design method to improve the transient response performance of a closed-loop reference model (CRM) adaptive control system. The methodology, known as RL-CRM, relies on the generation of a dynamic adaption strategy by implementing RL on the variable factor in the feedback path gain matrix of the reference model. An actor-critic RL agent is designed using the performance-driven reward functions and tracking error observations from the environment. In the training phase, a deep deterministic policy gradient algorithm is utilized to learn the time-varying adaptation strategy of the design parameter in the reference model feedback gain matrix. The proposed control structure provides the possibility to learn numerous adaptation strategies across a wide range of flight and vehicle conditions instead of being driven by high-fidelity simulators or flight testing and real flight operations. The performance of the proposed system was evaluated on an identified and verified mathematical model of an agile quadrotor platform. Monte-Carlo simulations and worst case analysis were also performed over a benchmark helicopter example model. In comparison to the classical model reference adaptive control and CRM-adaptive control system designs, the proposed RL-CRM adaptive flight control system design improves the transient response performance on all associated metrics and provides the capability to operate over a wide range of parametric uncertainties.     

Adaptive iterative learning control of discrete‐time varying systems with unknown control direction

Without using Nussbaum gain, a novel method is presented to solve the unknown control direction problem for discrete‐time systems. The underlying idea is to fully exploit the convergence property of parameter estimates in well‐known adaptive algorithms. By incorporating two modifications into the control and the parameter update laws, respectively, we present an adaptive iterative learning control scheme for discrete‐time varying systems without the prior knowledge of the sign of control gain. It is shown that the proposed adaptive iterative learning control can achieve perfect tracking over the finite time interval while all the closed‐loop signals remain bounded. An illustrative example is presented to verify effectiveness of the proposed scheme. Copyright © 2012 John Wiley & Sons, Ltd.     

Switching‐based state tracking of model reference adaptive control systems in the presence of intermittent failures of all actuators

This paper investigates the state tracking problem for a class of model reference adaptive control systems with intermittent failures of all actuators. We consider the case that all actuators may suffer failures simultaneously. The concepts of failure frequency and unavailability rate are introduced to describe the failures. Because of the actuator failures, the error system is modeled as a switched system. Then, the notion of global practical stability of switched systems is presented, and sufficient conditions are provided to guarantee the global practical stability of the error system. An example of HiMAT vehicle and the simulation results demonstrate the feasibility and effectiveness of the proposed design method. Copyright © 2013 John Wiley & Sons, Ltd.     

Direct adaptive control for non‐linear uncertain systems with exogenous disturbances

A direct adaptive non‐linear control framework for multivariable non‐linear uncertain systems with exogenous bounded disturbances is developed. The adaptive non‐linear controller addresses adaptive stabilization, disturbance rejection and adaptive tracking. The proposed framework is Lyapunov‐based and guarantees partial asymptotic stability of the closed‐loop system; that is, asymptotic stability with respect to part of the closed‐loop system states associated with the plant. In the case of bounded energy L₂ disturbances the proposed approach guarantees a non‐expansivity constraint on the closed‐loop input–output map. Finally, several illustrative numerical examples are provided to demonstrate the efficacy of the proposed approach. Copyright © 2002 John Wiley & Sons, Ltd.     

On necessary assumptions in discrete-time model reference adaptive control

In this paper we investigate the discrete-time model reference adaptive control problem, ascertain the extent to which the classical assumptions are necessary and provide several suitably modified inviolable requirements. In particular, we show that under a closed-loop causality constraint the problem is solvable only if there is an upper bound on the plant relative degree and the plant zeros outside the open unit disc lie in a finite set. We also derive a bound on the achievable asymptotic performance in the event that these requirements are not met.     

Model reference adaptive control for nonlinear switched systems under asynchronous switching

In this paper, the problem of model reference adaptive control for nonlinear switched systems with parametric uncertainties is investigated. Asynchronous switching between subsystems and adaptive controllers is also considered. Firstly, a state feedback adaptive controller is designed. Then, sufficient conditions ensuring the global practical stability of the error switched system with average dwell time are proposed. The boundedness of all signals in the closed‐loop system is guaranteed by the proposed adaptive controller. Finally, a practical example is given to demonstrate the validity of the main results. Copyright © 2016 John Wiley & Sons, Ltd.     

A new approach to model reference adaptive control

A new approach to model reference adaptive control, based on a combination of direct and indirect control methods, is introduced in this paper. The controller structure is identical to that used in the direct method, but the algorithm used to update the controller parameters depends both on the output error as in direct control and on the plant parameter estimates as in indirect control. The global stability of the overall system is assured by the existence of a Lyapunov function. In the ideal case discussed here, the combined approach results in improved transient response with smaller amplitude of the control input as compared to the constituent methods.     

A new decentralized model reference adaptive control for a class of interconnected dynamic systems using variable structure design

This paper presents a new decentralized model reference adaptive control for a class of large-scale interconnected dynamic systems. Interconnections among subsystems may be time-invariant or time-varying and linear or non-linear. The scheme proposed here only takes input and output measurements from each subsystem for input synthesis. Using a variable structure design concept, we show that the tracking errors will converge to zero in finite time despite the interconnections with any possible strengths.     

Model reference adaptive control with unknown relative degree

This work presents an indirect, model reference adaptive control for minimum phase linear systems of arbitrary relative degree. Global stability of the closed-loop system is proved in spite of bounded disturbances and asympotic tracking is achieved in the ideal case.     

Robust adaptive tracking control of uncertain discrete time systems

In this paper, the problem of robust adaptive tracking for uncertain discrete‐time systems is considered from the slowly varying systems point of view. The class of uncertain discrete‐time systems considered is subjected to both 𝓁_∞ to 𝓁_∞ bounded unstructured uncertainty and external additive bounded disturbances. A priori knowledge of the dynamic model of the reference signal to be tracked is not completely known. For such problem, an indirect adaptive tracking controller is obtained by frozen‐time controllers that at each time optimally robustly stabilize the estimated models of the plant and minimize the worst‐case steady‐state absolute value of the tracking error of the estimated model over the model uncertainty. Based on 𝓁_∞ to 𝓁_∞ stability and performance of slowly varying system found in the literature, the proposed adaptive tracking scheme is shown to have good robust stability. Moreover, a computable upper bound on the size of the unstructured uncertainty permitted by the adaptive system and a computable tight upper bound on asymptotic robust steady‐state tracking performance are provided. Copyright © 2005 John Wiley & Sons, Ltd.     

Improving transient performance of discrete-time model reference adaptive control architectures

Discrete-time adaptive control algorithms can be executed directly in embedded code unlike their continuous-time counterparts, which require discretization. However, their designs predicated on quadratic Lyapunov-based frameworks are quite intricate due to the resulting complexity in the Lyapunov difference expressions. Therefore, a wide array of available continuous-time results addressing transient performance issues using adaptive control algorithms cannot be applied or readily extended to the discrete-time case. In this article, we present a new model reference adaptive control architecture for discrete-time uncertain dynamical systems. Specifically, the proposed architecture consists of a command governor mechanism that adjusts the trajectory of a given command during the closed-loop transient response. It is shown that this mechanism is effective in improving transient performance of discrete-time model reference adaptive control architectures. Using a logarithmic Lyapunov function, we prove Lyapunov stability of the closed-loop system as well as asymptotic convergence of the system error states involving the difference between the states of the uncertain dynamical system and the states of the reference model, as well as driving the command governor signal to zero.     

Discrete‐time periodic adaptive control for parametric systems with non‐sector nonlinearities

In this paper, a periodic adaptive control approach is proposed for a class of discrete‐time parametric systems with non‐sector nonlinearities. The proposed periodic adaptive control law is characterized by either one‐period delayed parametric updating or two‐period delayed parametric updating when input gain contains periodic unknowns. Logarithmic‐type discrete Lyapunov function is employed to handle the difficulties caused by the uncertainties that do not satisfy the linear growth condition. Some extensions to nonlinear systems with multiple unknown parameters and time‐varying input gain, tracking tasks, as well as higher‐order systems in canonical form, are also discussed. Copyright © 2013 John Wiley & Sons, Ltd.     

Fractional order model reference adaptive control for anesthesia

The design of a fractional order model reference adaptive control for anesthesia based on a fractional order model is proposed in the paper. This model gets around many difficulties in controller designs based on the pharmacokinetic/pharmacodynamic model, commonly used for anesthesia for theses purposes, and allows to design a simple adaptive controller with stability and positivity of the system ensured via Lyapunov analysis. Also, the convergence of the tracking error to zero is established by applying an extension of the Barbalat lemma, proven in the paper. Simulations illustrate the effectiveness and robustness of the proposed control.