# Adaptive Control, Overview

**DOI:**https://doi.org/10.1007/978-1-4471-5102-9_110-1

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## Keywords

Adaptive control Estimation## Introduction

### What Is Adaptive Control

Feedback control has a long history of using sensing, decision, and actuation elements to achieve an overall goal. The general structure of a control system may be illustrated in Fig. 1. It has long been known that high fidelity control relies on knowledge of the system to be controlled. For example, in most cases, knowledge of the plant gain and/or time constants (represented by *θ* _{ p } in Fig. 1) is important in feedback control design. In addition, disturbance characteristics (e.g., frequency of a sinusoidal disturbance), *θ* _{ d } in Fig. 1, are important in feedback compensator design.

Many control design and synthesis techniques are model based, using prior knowledge of both model structure and parameters. In other cases, a fixed controller structure is used, and the controller parameters, *θ* _{ C } in Fig. 1, are tuned empirically during control system commissioning. However, if the plant parameters vary widely with time or have large uncertainties, these approaches may be inadequate for high-performance control.

- 1.
Robust control (“Optimization Based Robust Control” (Henrion)), wherein a controller is designed to perform adequately despite the uncertainties. Variable structure control may have very high levels of robustness in some cases and therefore is a special class of robust nonlinear control.

- 2.
Adaptive control, where the controller learns and adjusts its strategy based on measured data. This frequently takes the form where the controller parameters,

*θ*_{ C }, are time-varying functions that depend on the available data (*y*(*t*),*u*(*t*), and*r*(*t*)). Adaptive control has close links to intelligent control (including neural control (Neural Control and Approximate Dynamic Programming (Lewis)), where specific types of learning are considered) and also to stochastic adaptive control (Stochastic Adaptive Control (Duncan)).

Robust control is most useful when there are large unmodeled dynamics (i.e., structural uncertainties), relatively high levels of noise, or rapid and unpredictable parameter changes. Conversely, for slow or largely predictable parameter variations, with relatively well-known model structure and limited noise levels, adaptive control may provide a very useful tool for high- performance control (Åström and Wittenmark 2008).

## Varieties of Adaptive Control

One practical variant of adaptive control is controller auto-tuning (Autotuning (Hagglund)). Auto-tuning is particularly useful for PID and similar controllers and involves a specific phase of signal injection, followed by analysis, PID gain computation, and implementation. These techniques are an important aid to commissioning and maintenance of distributed control systems.

There are also large classes of adaptive controllers that are continuously monitoring the plant input-output signals to adjust the strategy. These adjustments are often parametrized by a relatively small number of coefficients, *θ* _{ C }. These include schemes where the controller parameters are directly adjusted using measureable data (also referred to as “implicit,” since there is no explicit plant model generated). Early examples of this often included model reference adaptive control (Model Reference Adaptive Control (Sun)). Other schemes (Middleton et al. 1988) explicitly estimate a plant model *θ* _{ P }; thereafter, performing online control design and, therefore, the adaptation of controller parameters *θ* _{ C } are indirect. This then led on to a range of other adaptive control techniques applicable to linear systems (Adaptive Control of Linear Time Invariant Systems (Ioannou)).

There have been significant questions concerning the sensitivity of some adaptive control algorithms to unmodeled dynamics, time-varying systems, and noise (Ioannou and Kokotovic 1984; Rohrs et al. 1985). This prompted a very active period of research to analyze and redesign adaptive control to provide suitable robustness (Robust Adaptive Control (Annaswamy)) (e.g., Anderson et al. 1986; Ioannou and Sun 2012) and parameter tracking for time-varying systems (Adaptive Control of Time Varying Systems (Tsakalis)) (e.g., Kreisselmeier 1986; Middleton and Goodwin 1988).

Work in this area further spread to nonparametric methods, such as switching, or supervisory adaptive control (Switching Adaptive Control (Fu)) (e.g., Fu and Barmish 1986; Morse et al. 1992). In addition, there has been a great deal of work on the more difficult problem of adaptive control for nonlinear systems (Nonlinear Adaptive Control (Astolfi)).

A further adaptive control technique is extremum seeking control (Extremum Seeking Control (Krstic)). In extremum seeking (or self optimizing) control, the desired reference for the system is unknown, instead we wish to maximize (or minimize) some variable in the system (Ariyur and Krstic 2003). These techniques have quite distinct modes of operation that have proven important in a range of applications.

A final control algorithm that has nonparametric features is iterative learning control (Iterative Learning Control (Owens)) (Amann et al. 1996; Moore 1993). This control scheme considers a system with a highly structured, namely, repetitive finite run, control problem. In this case, by taking a nonparametric approach of utilizing information from previous run(s), in many cases, near-perfect asymptotic tracking can be achieved.

Adaptive control has a rich history (History of Adaptive Control (Astrom)) and has been established as an important tool for some classes of control problems.

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