Adaptive Control with Unknown Parameters in Reference Input

This work proposes a distributed composite adaptive synchronization algorithm for multiple uncertain EulerLagrange (EL) systems, where parameter convergence is achieved under a relaxed mathematical condition as compared to the state-of-the-art. Classical adaptive controllers require an analytical condition, called persistence of excitation (PE), to ensure parameter convergence, which results in better transient performance and robustness to disturbance. The PE condition is extended to Cooperative-PE (C-PE) condition for distributed adaptive controllers with cooperative estimation strategies. The PE and C-PE conditions are restrictive in nature since these conditions are not satisfied in most practical applications. Recent literature in adaptive control has relaxed the PE condition to Initial Excitation (IE), which is shown to be sufficient for parameter convergence. The IE condition is argued to be significantly milder than PE and can be satisfied in many practical setting. The proposed result further extends the IE condition to Cooperative-IE (C-IE) condition in distributed adaptive control architecture in the context of synchronizing multiple EL systems. It is established that the C-IE condition is milder than PE, IE, and C-PE conditions. Two-tier filter based estimation algorithm with strategic switching ensures parameter convergence under the C-IE condition and thereby provides exponential convergence of tracking and parameter estimation error to zero. Simulation results validate the efficacy of the proposed algorithm as compared to conventional distributed adaptive controllers in terms of superior tracking and estimation performance.

Implicit function based adaptive control of non-canonical form discrete-time nonlinear systems

formula omitted] model reference adaptive control for switched systems based on the switched closed-loop reference model

Composite anti-disturbance model reference adaptive control for switched systems

SummaryThis paper investigates the robust resilient control problem for a class of parametric strict feedback nonlinear systems with prescribed output and virtual tracking errors performance. The resilience is governed by a continuously nonlinear control gains function, which endows the virtual and actual controllers with self‐adjusting abilities with respect to transformed error surfaces. The proposed control scheme is adaptation, estimation, and approximation‐free in the presence of unknown parameters and nonlinearities, and only a number of control gains, which is equal to the relative degree of the considered plants, need to be selected in applications. It is proved by rigorous analysis that the output tracking errors are confined in predefined prescribed performance functions under some nonrestrictive initial conditions, and the bounds of states are obtained characterized as control gains and systemic function‐associated constants. Finally, comparative illustrative examples are given to demonstrate the effectiveness of the proposed control scheme.

This paper investigates the H∞ state tracking model reference adaptive control (MRAC) problem for a class of switched systems using an average dwell-time method. First, a stability criterion is established for a switched reference model. Then, an adaptive controller is designed and the state tracking control problem is converted into the stability analysis. The global practical stability of the error switched system can be guaranteed under a class of switching signals characterised by an average dwell time. Consequently, sufficient conditions for the solvability of the H∞ state tracking MRAC problem are derived. An example of highly manoeuvrable aircraft technology vehicle is given to demonstrate the feasibility and effectiveness of the proposed design method.

This paper addresses the problem of designing an output error feedback control for single-input, single-output nonlinear systems with uncertain, smooth, output-dependent nonlinearities whose local Lipschitz constants are known. The considered systems are required to be observable, minimum phase with known relative degree and known high frequency gain sign: linear systems are included. The reference output signal is assumed to be smooth and periodic with known period. By developing in Fourier series expansion a suitable periodic input reference signal, an output error feedback adaptive learning control is designed which ldquolearnsrdquo the input reference signal by identifying its Fourier coefficients: bounded closed loop signals and exponential tracking of both input and output reference signals are obtained when the Fourier series expansion is finite, while arbitrary small tracking errors are exponentially achieved otherwise. The resulting control is not model based, is independent of the system order and depends only on the relative degree, the reference signal period and the high frequency gain sign.

This paper explores the model reference adaptive control problem for a class of switched linear systems under arbitrary switching with no need for the measurability of the system state. Based on the state of reference model and the measurable output error, adaptive laws and controllers are designed for switched systems. Each subsystem may have its individual reference model and controller, which increases the design flexibility. The introduction of the closed-loop reference model is to get a better transient performance of the whole switched systems. A numerical example is provided to verify the effectiveness of the main results.

SummarySeveral cooperative driving strategies proposed in literature, sometimes known as cooperative adaptive cruise control strategies, assume that both relative spacing and relative velocity with preceding vehicle are available from on‐board sensors (laser or radar). Alternatively, these strategies assume communication of both velocity states and acceleration inputs from preceding vehicle. However, in practice, on‐board sensors can only measure relative spacing with preceding vehicle (since getting relative velocity requires additional filtering algorithms); also, reducing the number of variables communicated from preceding vehicle is crucial to save bandwidth. In this work we show that, after framing the cooperative driving task as a distributed model reference adaptive control problem, the platooning task can be achieved in a minimal sensing and communication scenario, that is, by removing relative velocity measurements with preceding vehicle and by removing communication from preceding vehicle of velocity states. In the framework we propose, vehicle parametric uncertainty is taken into account by appropriately designed adaptive laws. The proposed framework is illustrated and shown to be flexible to several standard architectures used in cooperative driving (one‐vehicle look‐ahead topology, leader‐to‐all topology, multivehicle look‐ahead topology).

Robust Adaptive Control

Adaptive Tracking Control of Rigid Robot Manipulators by Using Only Joint Position Measurements

This paper design an output tracking controller for a class of uncertain nonlinear systems to address the input quantization and output tracking funnel control problem. By the traditional adaptive control and backstepping technique, an adaptive quantized funnel control scheme is designed. It is shown that the presented controller can ensure that arbitrary closed-loop signals are globally uniformly bounded, and the output tracking error is bounded, and held in the prescribed funnel performance functions. The presented control scheme is checked through the simulation result.

This paper proposes a dual adaptive control methodology for extremum control of stochastic Hammerstein systems that are subject to uncertainty and characterised by a nonlinear second-order polynomial function. The design is based on an explicit-type innovations dual cost function that leads to a control law which balances out the need for caution when using uncertain parameter estimates to effect control actions, with the conflicting need to probe the system input so as to reduce parameter uncertainty. This extremum control problem is more challenging than conventional adaptive systems because the reference input is itself a non-linear function of the unknown system parameters. The controller's performance is analysed through extensive Monte Carlo simulations and shown to be superior to other types of adaptive control systems that use a certainty equivalence assumption.

New approximative assumption of the partial certainty equivalence (PCE) has been suggested for adaptive control of nonlinear and linear stochastic systems. For derivation of a suboptimal controller with the PCE the certainty equivalence (CE) assumption is used only for the part of the system states and unknown parameters. The PCE control policy has a simple form for linear systems with unknown parameters. At the same time it provides cautious system behaviour and some persistent excitation required. It is suggested in the present paper to design adaptive control using the PCE assumption and bicriterial optimization for providing the optimal persistent excitation. Thus a dual controller will be derived. The synthesis problem is formulated for general nonlinear systems and considered for linear systems in details. The resulting controller demonstrates improved system behaviour and short time of adaptation. A simulated example is used to demonstrate the potential of the suggested method and its superiority over the PCE and the usually applied CE policies.

This work generalizes the recently developed initial excitation (IE) based adaptive control by introducing the notion of semi-initial excitation (semi-IE), a still relaxed version of IE. Typically, classical adaptive controllers guarantee Lyapunov stability of the overall error dynamics (tracking error + parameter estimation error) and asymptotic convergence of tracking error to zero, while requiring a restrictive condition of persistence of excitation (PE) for parameter convergence. The authors' recent work on a new adaptive control architecture based on the milder IE condition guarantees parameter convergence while ensuring exponential stability of the overall error dynamics once the online verifiable IE condition is satisfied. The current work further relaxes the excitation condition by proposing the concept of semi-IE. The proposed adaptive controller is proved to guarantee convergence of the parameter estimation error to a lower dimensional manifold under the weaker semi-IE condition, while the stronger condition of IE guarantees convergence of the parameter estimation error to zero. The designed adaptive algorithm has been shown to significantly improve the transient response of tracking error as compared to the conventional approaches.