The book provides a comprehensive introduction to NMPC and nonlinear adaptive control. In the first part of the book, a framework for the study, design, and analysis of NMPC systems is presented. The robustness of NMPC is presented in the context of this framework. The second part of the book presents an introduction to adaptive NMPC. Starting with a basic introduction to the problems associated with adaptive MPC, a robust set-based approach is developed. The third part of the book is dedicated to the practical realization of the adaptive NMPC methodology. An alternative approach to adaptive parameter estimation is first developed that yields a systematic set-based parameter estimation approach.The last part of the book presents a treatment of the discrete-time generalization of the continuous-time algorithms proposed in the third part of the book.

The ultimate objective of a model predictive controller is to provide a closed-loop feedback that regulates to its target set in a fashion that is optimal with respect to the infinite-time problem, while enforcing pointwise constraints in a constructive manner.

The vast majority of MPC implementations are based upon the approximation as being PWC in time, making use of a zero-order hold both in the input implementation as well as in the model predictions. From a theoretical perspective, there is nothing preventing the use of more general parameterizations to describe sub-arcs when implemented within a SD framework. In general, higher-order parameterizations involving increased number of parameters (per interval) are able to describe up over significantly longer intervals, resulting in an overall decrease in the number of parameters required to comparably describe. However, the open-loop nature of the SD intervals requires that their duration be kept reasonably short, thereby eliminating most of the benefits associated with increasing the order of the parameterization. As such, it is rarely practical for SD control designs to make use of any parameterizations beyond the basic PWC selection.

The control objective is to feasibly stabilize x to a given compact set, that is not necessarily robustly invariant with respect to the full uncertainty. It is assumed that a set and instantaneous cost are selected. The robust control design proposed depends on the knowledge of appropriate Lipschitz bounds for the x-dependence of the dynamics f (x, u) and g(x, u), and for the penalty functions L(x, u) and W(x, O).

The FT identification method has two distinguishing features. First, the true parameter estimate is obtained at any time instant the excitation condition is satisfied, and second, the procedure allows for a direct and immediate removal of any perturbation signal injected into the closed-loop system to aid in parameter estimation. However, the drawback of the FT identification algorithm is the requirement to check the invertibility of a matrix online and compute the inverse matrix when appropriate. To avoid these concerns and enhance the applicability of the FT method in practical situations, the procedure is hereby exploited to develop a novel adaptive compensator that (almost) recovers the performance of the FTI. The compensator guarantees exponential convergence of the parameter estimation error at a rate dictated by the closed-loop system's excitation. It was shown how the adaptive compensator can be used to improve upon existing adaptive controllers. The modification proposed guarantees exponential stability of the parametric equilibrium provided the given PE condition is satisfied. Otherwise, the original system's closed-loop properties are preserved.

In general, modeling error consists of parametric and non-parametric uncertainties and the system dynamics can be influenced by exogenous disturbances as well. In this chapter, we extend the adaptive MPC framework presented in Chapter 10 to nonlinear systems with both constant parametric uncertainty and additive exogenous disturbances. Intuitively, an adaptive controller should lead to controller with better robustness properties than their non-adaptive counterpart since they use more information on the systems uncertainties. However, this is not generally the case. Under external disturbance input, adaptive controllers can lead to inferior transient behavior, infinite parameter drift, and burstiness in the closed-loop system. To address these problems, parameter projection is used to ensure the estimate remains in a convex set and the parameter estimates are updated only when an improved estimate is obtained. The formulation provides robustness to parameter estimation error and bounded disturbances E V. While the disturbance set V remains unchanged over time, the parametric uncertainty set Θ is adapted in such a way that guarantees its contraction.

This article presents new techniques for parameter identification for nonlinear dynamical discrete-time systems. The methods presented are intended to improve the performance of adaptive control systems such as RTO schemes and adaptive extremum-seeking systems. Using recent results on FT adaptive control, we develop alternative techniques that can be used to guarantee the convergence of parameter estimates to their true values in the presence of model-mismatch and exogenous variables. Three methods are presented. The first two methods rely on system excitation and a regressor matrix, in either case, the true parameters are identified when the regressor matrix is of full rank and can be inverted. The third method is based on a novel set-based adaptive estimation method proposed in Chapter 10 to simultaneously estimate the parameters and the uncertainty associated with the true value. The uncertainty set is updated periodically when sufficient information has been obtained to shrink the uncertainty set around the true parameters. Each method guarantees convergence of the parameter estimation error, provided an appropriate PE condition is met. The effectiveness of each method is demonstrated using a simulation example, displaying convergence of the parameter error estimation error.