Relatively suboptimal control: A scenario approach to constrained control design

A particular control scenario is sometimes important for a plant when for example the plant is controlled from a given point to another. In this case, optimal constrained feedback control design can be dramatically simplified, which is recently proposed as relatively optimal control (ROC). The ROC ensures stability of the closed-loop system and optimality for a given initial state of the plant. This paper presents relatively suboptimal control (RSOC), which is an extension of the ROC to the case that a set of scenarios, i.e., a set of optimal trajectories is given. The derived linear feedback controller ensures stability of the closed-loop system and generates state trajectories close to these scenarios in the sense of a quadratic performance index. The order of the proposed controller is independent of the number of the scenarios.