Suboptimal solutions to restricted-control LQR problems

COSTANZA, V; PABLO S. RIVADENEIRA

Buenos Aires

Congreso; 23º Congreso Argentino de Congreso Automático; 2012

AADECA

The optimal solution for a given process with restricted controls, starting at a known initial state, is shown to coincide with the saturated solution to some unrestricted problem that has the same coefficients, except for the final penalization matrix S, and starts at a generally different initial state. This result reduces the searching span for the solution: from the infinite-dimensional set of admissible control trajectories, to the finite-dimensional space of symmetric positive semi-definite symmetric matrices ˆ S and initial states ˆx0. An efficient scheme is proposed to approximate (eventually to find) the optimal feedback strategy on-line, based on the updating of ˆ S at successive sampling times tk, and on the possibility to generate the corresponding Riccati matrix P(t, T, ˆ S) for tk < t ≤ tk+1 from auxiliary matrices stored in memory. Numerical simulations are provided, compared, and checked against the analytical solutions of a two-dimensional case-study.S, and starts at a generally different initial state. This result reduces the searching span for the solution: from the infinite-dimensional set of admissible control trajectories, to the finite-dimensional space of symmetric positive semi-definite symmetric matrices ˆ S and initial states ˆx0. An efficient scheme is proposed to approximate (eventually to find) the optimal feedback strategy on-line, based on the updating of ˆ S at successive sampling times tk, and on the possibility to generate the corresponding Riccati matrix P(t, T, ˆ S) for tk < t ≤ tk+1 from auxiliary matrices stored in memory. Numerical simulations are provided, compared, and checked against the analytical solutions of a two-dimensional case-study.S and initial states ˆx0. An efficient scheme is proposed to approximate (eventually to find) the optimal feedback strategy on-line, based on the updating of ˆ S at successive sampling times tk, and on the possibility to generate the corresponding Riccati matrix P(t, T, ˆ S) for tk < t ≤ tk+1 from auxiliary matrices stored in memory. Numerical simulations are provided, compared, and checked against the analytical solutions of a two-dimensional case-study.S at successive sampling times tk, and on the possibility to generate the corresponding Riccati matrix P(t, T, ˆ S) for tk < t ≤ tk+1 from auxiliary matrices stored in memory. Numerical simulations are provided, compared, and checked against the analytical solutions of a two-dimensional case-study.P(t, T, ˆ S) for tk < t ≤ tk+1 from auxiliary matrices stored in memory. Numerical simulations are provided, compared, and checked against the analytical solutions of a two-dimensional case-study.. Numerical simulations are provided, compared, and checked against the analytical solutions of a two-dimensional case-study.