Second-Order NonConvex Optimization for Constrained Fixed-Structure Static Output Feedback Controller Synthesis

For linear time-invariant systems, the design of an optimal controller is a commonly encountered problem in many applications. Among all optimization approaches available, quadratic regulator (LQR) methodology certainly garners much attention and interest. As well known, standard numerical tools algebra are readily available to determine static LQR feedback gain matrix when system state variables measurable. However, various certain scenarios where some not measurable, consequent prescribed structural constraints on structure arise, can become intractable due nonconvexity characteristics that then be present. In such cases, first-order methods have been proposed cater these problems, but methods, if at successful, limited convergence. To speed up convergence, second-order approach space essential, with appropriate solve equality constrained output (SOF) suitably defined cost function. Thus, this article, efficient method calculate Hessian by solving several Lyapunov equations. Then, new technique applied deal indefiniteness matrix. Subsequently, through Newton’s constraints, algorithm developed effectively SOF problem. Finally, two examples described, which demonstrate applicability effectiveness method.