Adaptive Control By Regulation-Triggered Batch Least-Squares Estimation of Non-Observable Parameters

The paper extends a recently proposed indirect, certainty-equivalence, event-triggered adaptive control scheme to the case of non-observable parameters. The extension is achieved by using a novel Batch Least-Squares Identifier (BaLSI), which is activated at the times of the events. The BaLSI guarantees the finite-time asymptotic constancy of the parameter estimates and the fact that the trajectories of the closed-loop system follow the trajectories of the nominal closed-loop system ("nominal" in the sense of the asymptotic parameter estimate, not in the sense of the true unknown parameter). Thus, if the nominal feedback guarantees global asymptotic stability and local exponential stability, then unlike conventional adaptive control, the newly proposed event-triggered adaptive scheme guarantees global asymptotic regulation with a uniform exponential convergence rate. The developed adaptive scheme is tested to a well-known control problem: the state regulation of the wing-rock model. Comparisons with other adaptive schemes are provided for this particular problem.Comment: 29 pages, 12 figure

Deadzone-Adapted Disturbance Suppression Control for Global Practical IOS and Zero Asymptotic Gain to Matched Uncertainties

In this paper we study a special class of systems: time-invariant control systems that satisfy the matching condition for which no bounds for the disturbance and the unknown parameters are known. For this class of systems, we provide a simple, direct, adaptive control scheme that combines three elements: (a) nonlinear damping, (b) single-gain adjustment, and (c) deadzone in the update law. It is the first time that these three tools are combined and the proposed controller is called a Deadzone-Adapted Disturbance Suppression (DADS) Controller. The proposed adaptive control scheme achieves for the first time an attenuation of the plant state to an assignable small level, despite the presence of disturbances and unknown parameters of arbitrary and unknown bounds. Moreover, the DADS Controller prevents gain and state drift regardless of the size of the disturbance and unknown parameter.Comment: 26 pages, 3 figure

Optimal adaptive control of time-delay dynamical systems with known and uncertain dynamics

Delays are found in many industrial pneumatic and hydraulic systems, and as a result, the performance of the overall closed-loop system deteriorates unless they are explicitly accounted. It is also possible that the dynamics of such systems are uncertain. On the other hand, optimal control of time-delay systems in the presence of known and uncertain dynamics by using state and output feedback is of paramount importance. Therefore, in this research, a suite of novel optimal adaptive control (OAC) techniques are undertaken for linear and nonlinear continuous time-delay systems in the presence of uncertain system dynamics using state and/or output feedback. First, the optimal regulation of linear continuous-time systems with state and input delays by utilizing a quadratic cost function over infinite horizon is addressed using state and output feedback. Next, the optimal adaptive regulation is extended to uncertain linear continuous-time systems under a mild assumption that the bounds on system matrices are known. Subsequently, the event-triggered optimal adaptive regulation of partially unknown linear continuous time systems with state-delay is addressed by using integral reinforcement learning (IRL). It is demonstrated that the optimal control policy renders asymptotic stability of the closed-loop system provided the linear time-delayed system is controllable and observable. The proposed event-triggered approach relaxed the need for continuous availability of state vector and proven to be zeno-free. Finally, the OAC using IRL neural network based control of uncertain nonlinear time-delay systems with input and state delays is investigated. An identifier is proposed for nonlinear time-delay systems to approximate the system dynamics and relax the need for the control coefficient matrix in generating the control policy. Lyapunov analysis is utilized to design the optimal adaptive controller, derive parameter/weight tuning law and verify stability of the closed-loop system”--Abstract, page iv

Least Squares Based Adaptive Control and Extremum Seeking with Active Vehicle Safety System Applications

On-line parameter estimation is one of the two key components of a typical adaptive control scheme, beside the particular control law to be used. Gradient and recursive least squares (RLS) based parameter estimation algorithms are the most widely used ones among others. Adaptive control studies in the literature mostly utilize gradient based parameter estimators for convenience in nonlinear analysis and Lyapunov analysis based constructive design. However, simulations and real-time experiments reveal that, compared to gradient based parameter estimators, RLS based parameter estimators, with proper selection of design parameters, exhibit better transient performance from the aspects of speed of convergence and robustness to measurement noise. One reason for the control theory researchers' preference of gradient algorithms to RLS ones is that there does not exist a well-established stability and convergence analysis framework for adaptive control schemes involving RLS based parameter estimation. Having this fact as one of the motivators, this thesis is on systematic design, formal stability and convergence analysis, and comparative numerical analysis of RLS parameter estimation based adaptive control schemes and extension of the same framework to adaptive extremum seeking, viz. adaptive search for (local) extremum points of a certain field. Extremum seeking designs apply to (i) finding locations of physical signal sources, (ii) minimum or maximum points of (vector) cost or potential functions for optimization, (iii) calculating optimal control parameters within a feedback control design. In this thesis, firstly, gradient and RLS based on-line parameter estimation schemes are comparatively analysed and a literature review on RLS estimation based adaptive control is provided. The comparative analysis is supported with a set of simulation examples exhibiting transient performance characteristics of RLS based parameter estimators, noting absence of such a detailed comparison study in the literature. The existing literature on RLS based adaptive control mostly follows the indirect adaptive control approach as opposed to the direct one, because of the difficulty in integrating an RLS based adaptive law within the direct approaches starting with a certain Lyapunov-like cost function to be driven to (a neighborhood) of zero. A formal constructive analysis framework for integration of RLS based estimation to direct adaptive control is proposed following the typical steps for gradient adaptive law based direct model reference adaptive control, but constructing a new Lyapunov-like function for the analysis. After illustration of the improved performance with RLS adaptive law via some simple numerical examples, the proposed RLS parameter estimation based direct adaptive control scheme is successfully applied to vehicle antilock braking system control and adaptive cruise control. The performance of the proposed scheme is numerically analysed and verified via Matlab/Simulink and CarSim based simulation tests. Similar to the direct adaptive control works, the extremum seeking approaches proposed in the literature commonly use gradient/Newton based search algorithms. As an alternative to these search algorithms, this thesis studies RLS based on-line estimation in extremum seeking aiming to enhance the transient performance compared to the existing gradient based extremum seeking. The proposed RLS estimation based extremum seeking approach is applied to active vehicle safety system control problems, including antilock braking system control and traction control, supported by Matlab/Simulink and CarSim based simulation results demonstrating the effectiveness of the proposed approach