Robust adaptive control of deterministic and stochastic strict-feedback systems

This thesis investigates several topics involving robust adaptive control of uncertain, partially unknown nonlinear systems in strict-feedback form, with deterministic as well as stochastic formulations.; The first topic studied in this thesis is the problem of robust controller design for a class of single-input single-output nonlinear systems in strict-feedback form with structurally unknown dynamics and also with unknown virtual control coefficients. The unknown nonlinearities in the system dynamics are approximated in terms of a family of basis functions, with the only crucial assumption made being that the parameters that characterize such a neural-network based approximation lie in some known compact sets. In this setup, a robust state-feedback controller is designed such that the system output tracks a given signal arbitrarily well, and all signals in the closed-loop system remain bounded. Moreover, a relevant disturbance attenuation inequality is satisfied by the closed-loop signals. These results are then extended to the case where only the output variable is available for feedback. In this case, for tractability, the nonlinear functions in the system dynamics are restricted to depend only on the measured output variable, which results in a strict output-feedback form.; The second topic studied involves control of stochastic nonlinear systems with parametric uncertainty. The class of systems considered are single-input single-output and in strict-feedback form, with the performance measured with respect to a risk-sensitive cost criterion. The uncertainty in the system description is assumed to be linearly parameterized, where the unmeasured parameters are generated by a stochastic differential equation. By employing the backstepping design technique, a state-feedback adaptive controller is constructed, which maintains an arbitrarily small average value for the risk-sensitive cost. The controller designed achieves boundedness in probability for all closed-loop signals, and under certain conditions the tracking error converges to zero almost surely. These results are also extended to the output-feedback case by employing the backstepping technique on the estimates of the unmeasured states provided by a simple state estimator.; The third topic studied involves decentralized control of uncertain systems. The class of systems focussed on is a set of stochastic strict-feedback systems which interact through their outputs, and performance is measured again with respect to a risk-sensitive cost criterion. The unknown nonlinear interconnection terms are assumed to be bounded by some known functions of the outputs of the subsystems, multiplied by some unknown parameters. The controllers designed for each subsystem have access only to the information available with regard to the respective subsystem, and they achieve an arbitrarily small value for the risk-sensitive cost for the overall system. Under this completely decentralized control scheme, all closed-loop signals remain bounded in probability.