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In this chapter, we present examples that illustrate the stability robustness properties of the safe adaptive control algorithm in the high uncertainty setting, and compare it with alternative control schemes. The motivating example gives insight into the model mismatch stability failure associated with model based adaptive control schemes lacking the necessary properties of their cost function, and a solution to the preceding problem is provided. Following this example, transient behavior improvement of the safe adaptive schemes is discussed. For completeness, some applications of the unfalsified control concept are reproduced in the last section of this chapter. [ABSTRACT FROM AUTHOR]

In this chapter, we lay out the foundations of the safe switching adaptive control theory, based on the controller falsification ideas. We study the properties of a closed loop switched adaptive system that employs an algorithm which prunes candidate controllers based on the information in the real-time measurement data. The goal of this pruning is to evaluate performance levels of the candidate controllers simultaneously before insertion into the closed loop. We formulate the list of the plant-independent properties of the cost function required for the stability guarantee. The crucial role of the cost detectability property is studied. We provide significant generalization by allowing the class of candidate controllers to have arbitrary cardinality, structure or dimensionality, and by strengthening the concept of tunability. Specialization to the linear time-invariant plants is discussed, giving insight into the bounds of the closed loop states. The extension to the time-varying plants is considered next, where cost detectability is shown to hold under modified conditions, and an upper bound on the number of switches over an arbitrary time period is derived. [ABSTRACT FROM AUTHOR]

In this chapter, we discuss the problem of the adaptive control and its present state of the art. We concern ourselves with the limitations of the adaptive control algorithms and discuss the tradeoff between the restrictions and benefits introduced by prior assumptions. Main contributions to the adaptive control within the last several decades are briefly reviewed to set up the stage for the current research results. We conclude the chapter by discussing the contribution of the monograph, which provides a solution to the long standing problem of model mismatch instability, cast in a parsimonious theoretical framework. [ABSTRACT FROM AUTHOR]

As robust control theory has matured, a key challenge has been the need for a more flexible theory that provides a unified basis for representing and exploiting evolving information flows from models, noisy data, and more. Our work on unfalsified control is providing a foundation for the development of such a theory. The results of research in progress are expected to facilitate the design of feedback control systems with the ability to better exploit evolving real-time information flows as they unfold, thereby endowing control systems with the intelligence to adapt to unfamiliar environments and to more effectively compensate for the uncertain and time-varying effects, equipment failures and other changing circumstances. [ABSTRACT FROM AUTHOR]

This article presents information on robust control systems. A robust control system is one that performs within specified tolerances despite uncertain variations in the controlled plant within given bounds. Robust control theory is that branch of mathematical system theory concerned with the design and analysis of robust feedback control systems. A gap between mathematical control theory and control engineering practice emerged in the 1960s and early 1970s, as the mathematical theory of feedback control increasingly decoupled from engineering practice. Time-tested root-locus and frequency-response techniques were regarded by researchers as ad hoc and simplistic.

Motivated by the heightened interest in adaptive learning control systems and a proliferation of results in nonlinear stability theory, the authors studied and presented the safe switching adaptive control of the highly uncertain systems. Those are the systems whose dynamics, parameters, or uncertainty models may be insufficiently known for a variety of reasons, including, for example, difficulty in obtaining accurate model estimates, changes in subsystem dynamics, component failures, external disturbances, time variation of plant parameters (slow but consistent time variation or infrequent large jumps) etc. [ABSTRACT FROM AUTHOR]