Control of second-order information for linear systems

Four controller design problems for linear systems are addressed. All these problems have several common features. (i) they are multi-objective designs, (ii) performance specifications and system uncertainties, if any, are given a priori, (iii) they have equivalent deterministic and stochastic meaning. The first problem is the covariance assignment problem. The whole set of steady state covariances X that a closed loop discrete system can possess is obtained. Furthermore, all controllers which assign this X to the system are parameterized in a closed form. The second problem addressed is the Output Variances Constrained (OVC) control problem. In this problem the minimum energy controller is designed to achieve prespecified output constraints. Necessary and sufficient conditions are derived for the optimal solution. A simple algorithm to solve this problem is also given, which has an important tuning property. This makes the lab test of the MIMO system more systematic. Instead of designing based on the nominal plant, the Robust Output Variances Constrained (ROVC) control problem considers the perturbations in the plant. The performance specifications required are the same as those in the OVC problem but should be satisfied for all admissible plants. A complete algorithm solving this problem is given. In this design, the admissible set, which is given a priori, is treated as a guide for this design algorithm. With the help of this guide, this algorithm, starting with a stability robust controller, carefully tunes the performance robustness of the closed loop system while maintaining the stability robustness. By noting that an output weighting matrix is the main design parameter for both the OVC algorithm and model reduction by Modal Cost Analysis (MCA), a design strategy is proposed which integrates both modeling and controller synthesis. In addition to this built-in model reduction technique, all software needed for this strategy is well developed and easy to carry out. Hence, it is very practical for the controller synthesis for Large Space Structures. This design strategy is applied to NASA\u27s Mini-Mast system, a standard Large Space Structure. Successful results are obtained on the first attempt