Nonlinear adaptive control of feedback passive systems
The authors apply to Yakubovich theory coming from the early 1970's, the concept of nonlinear adaptive control. Let the plant equations be: \(\dot x= F(x,u, \xi, v)\), \(y= H(x,u, \xi,v)\). Here \(x\), \(u\), \(y\) denote state, input and output vectors, \(\xi\) is the vector of parameters, \(v\) is an external disturbance. The control objective is given by: \(Q_t\leq 0\), \(t\geq t_n\). The authors wish to find a two-level algorithm such that the system meets its objective, while the trajectories belong to prescribed sets. The first level belongs to the main loop of the controlled system, and is called the control law. The second level forms the adaptation loop, and is called the adaptation law. The following cases are discussed separately: 1) Memoryless objective functional \(Q_t= Q(x, v)+ \overline {Q}\); 2) Integral objective functional; 3) Feedback passive system; 4) Adaptive feedback passivity. Theorems giving sufficient conditions for passivity and strict passivity of the output are proved. An example of a forced Lienard equation illustrates behavior of the output which depends on some choice for the parameters.
scientific article; zbMATH DE number 806691
scientific article