Study On The Achievement Of L₁ Optimal Control Method And The Compile Of MATLAB Lloptimal Toolbox

The optimal control problem addresses the design of optimal controllers, the objective is to find a LTI discrete-time controller that minimizes the induced norm of the transfer function relating the disturbances to the error signals of interest. Because the induced f norm of a transfer function corresponds to the \ norm of the impulse response, the resulting optimization problem is a norm minimization problem.Scaled method is a new calculation of the optimal control problem. After transferring the optimal control problem into the model match problem with the Youla parameter, scaled gets the answer of the optimal control problem through relative assistant problem, which is also a problem of infinite dimension and can be properly cut by the theory and the definite dimension line regulation problem can be solved, then the constringency limit can be gained. The final answer of the formal problem can be got through the connection between it and the assistant problem. So scaled-g is a simple and feasible calculation.Although the optimal control theory has been developed well and put into practice, the MATLAB has not supplied the relative toolbox and calculation functions. So I researched the solution proceed of the scaled-g, and gave the detailed steps of answering the optimal control problem. Furthermore, I wrote the relative functions in the key steps such as 'bezout' funtion in the Bezout equation, and supplied the order function to answer the optimal problems directly, so that achieved the function of outputting the result as soon as the parameter is inputted. At last I wrote the toolbox interphase named 11 optimal with the handle graphics supplied by MATLAB, in order that the users could use all the functions in the toolbox.