Adaptive control of dynamical systems on the basis of inverse problems of dynamics (Q1921531)

The paper discusses nonlinear control systems of the form \[ \dot x(t)= f(x(t),u(t),p(t)) \] with state \(x\in\mathbb{R}^n\), input \(u\in\mathbb{R}^m\), and unknown parameter vector \(p(t)\in\mathbb{R}^s\). The problem investigated consists in solving an optimal control problem for the dynamics in the presence of the unknown parameters. The solution is proposed as if \(p\) were known, and subsequently an adaptation law for an estimate of \(p\) is introduced. An example of a mathematical model of an aircraft illustrates the proposed methodology.