1. CONTROL with LIMITED INFORMATION Daniel Liberzon Coordinated Science Laboratory and Dept. of Electrical & Computer Eng., Univ. of Illinois at Urbana-Champaign CDC ’02

2. 0 Control objectives: stabilize to 0 or to a desired set containing 0, exit D through a specified facet, etc. CONSTRAINED CONTROL Constraint: – given control commands

3. LIMITED INFORMATION SCENARIO – partition of D – points in D, Quantizer/encoder: Control: for

4. PERTURBATION APPROACH 1.Design ignoring constraint 2.View as approximation 3.Prove that this still solves the problem Issue: error Need to be robust w.r.t. measurement errors

5. LINEAR SYSTEMS is asymptotically stable 9 Lyapunov function

6. LINEAR SYSTEMS (continued) To have ultimate bound we need

7. DYNAMIC QUANTIZATION After ultimate bound is achieved we can recompute partition for smaller region Zooming in and out, we recover global asymptotic stability zoom out zoom in

8. ACTIVE PROBING for INFORMATION Can achieve GAS if we recompute often enough.......... Related work: Wong-Brockett, Tatikonda-Mitter, Nair-Evans, Savkin-Petersen, Hespanha

9. RESEARCH DIRECTIONS Robust control design Facility location algorithms Performance (nonstandard criteria) Applications