Research On The Linear System Finite-time Optimal Tracking Control

Research on linear quadratic optimal control theory has been achieved plentifulresults, most of the research results are developed based on the infinite time linearquadratic performance index, while results on the finite-time linear quadratic optimalcontrol is not well studied yet. Compared to the infinite-time optimal controlfinite-time optimal control is more robust. Tracking control and disturbancesuppression control are frequently encountered problems in the modern control, sostudy on the tracking control and disturbance suppression control has importanttheoretical and practical significance. This thesis mainly studies the finite-timetracking control and finite-time disturbance suppression control of linear systems. Themain research contents are as follows:(1) Finite time optimal tracking control problem of linear systems is considered.According to the principle of minimum, finite-time optimal control law is obtained.Finally, numerical examples are provided, by comparison between finite-time andinfinite-optimal control simulation results, to show that this approach can achievebest tracking control.(2) Finite time suboptimal tracking control problem of linear systems isconsidered. By use of constant feedback gain in infinite time optimal control insteadof time-varying gain feedback gain in finite time optimal control and combiningstability degree stabilization method to remedy performance loss of sub-optimalcontrol, the suboptimal control law is obtained and better tracking control is achieved.Finally, numerical examples are provided to demonstrate this approach can achievebetter tracking control.(3) Output optimal tracking control for finite-time linear systems with continuousdisturbance signals is studied. And two forms is considered for the continuousdisturbance signals, one is the exponential decay, the other is the sinusoidal.According to the principle of minimum, finite-time optimal control law is obtained.Finally, numerical examples are provided, optimal tracking control simulation resultsfor the exponential decay signal and sinusoidal signal are obtained respectively, todemonstrate the effectiveness and feasibility of the proposed algorithm. (4) Output optimal tracking control for finite-time linear systems with continuousdisturbance is studied. By use of constant feedback gain in infinite time optimalcontrol instead of time-varying gain feedback gain in finite time optimal control andcombining stability degree stabilization method to remedy performance ofsub-optimal control, the suboptimal control law is obtained and better tracking controlis achieved. Finally, numerical examples are provided, optimal tracking controlsimulation results for the exponential decay signal and sinusoidal signal are obtainedrespectively, to demonstrate this approach can achieve better tracking control anddisturbance depressing control.