Roubst Control Research Of Parameter Time-Varying Linear System With Polytopic Uncertainty

"Min-Max" Robust control (i.e. Robust MPC) is a fashionable and effectivemethod for parameter time-varying linear system with polytopic uncertainty. With 20years' development, "Min-Max" robust control has held completely academicarchitecture. However, there still exist a lot of problems associated with theoreticanalyses and feasible operations, such as, larger available controlled stabilized initialconditions, better online performance and less complexity of online optimization. Inthis paper we investigate these left problems and subsequently hold a series of results.1,A new off-line "Min-Max" robust control algorithm is proposed for parametertime-varying linear system with polytopic uncertainty. Firstly, stable polytopicinvariant set with arbitrary given number of vertices is constructed to extend availablecontrolled stabilized initial conditions. Secondly, current control input is associatedwith the feedback laws in adjacent asymptotically stable polytopic invariant setsconstructed off-line one within another. Thirdly, only three linear equations arecomputed online to make this algorithm easily implemented in practical system.2,A new off-line "Quasi-Min-Max" robust control is proposed for "quasi"parameter time-varying linear system with polytopic uncertainty. Firstly, a parameter-dependent feedback law is designed in asymptotically stable polytopes computedoff-line to extend available controlled stabilized initial conditions. Secondly, onlineoptimization only includes several linear programming; the number of these linearprogramming is only associated with the number of asymptotically stable polytopicsets computed off-line and independent of the number of vertices of polytopicuncertainty and these off-line-computed polytopic stable sets.3,A new method for estimating the domain of attraction of the origin ispresented for parameter time-varying linear system with polytopic uncertainty under asaturated linear feedback. A simple condition is first derived in terms of an auxiliarycontrol input sequence for determining if a given polytope is asymptotically stableinvariant. Then a sufficient and necessary condition for stability polytope with a saturated linear feedback is presented for single input system.4,A new off-line "Min-Max" robust control is proposed for parametertime-varying linear system with polytopic uncertainty. With actuator saturatedfeedback law designed in asymptotically stable polytope off-line constructed onewithin another; the online performance will remarkably be promoted withoutadditional off-line and online complexity.5,A new quasi-infinite nonlinear stabilizing MPC is proposed with terminalstate inequality constraint and terminal cost. The feasibility of terminal stateinequality constraint implies the states at the end of the horizon are in a prescribedasymptotically stable but not necessarily invariant ellipsoidal set. The terminal statepenalty matrix of the terminal penalty item is to be chosen as time varying matrixparameter-dependent on the terminal state, which makes nonlinear MPC extendavailable stabilized initial conditions with holding satisfying online performance.