SWITCHING CONTROL DESIGN Daniel Liberzon Coordinated Science Laboratory and Dept. of Electrical & Computer Eng., Univ. of Illinois at Urbana-Champaign

HYBRID FEEDBACK Plant: P Classical continuous feedback paradigm: C P But logical decisions are often necessary: The closed-loop system is hybrid u y C1 C2 l o g i c P

REASONS for SWITCHING Nature of the control problem Sensor or actuator limitations Large modeling uncertainty Discuss all three briefly The first one: Brockett’s necessary condition One way out - hybrid feedback Combinations of the above

REASONS for SWITCHING Nature of the control problem Sensor or actuator limitations Large modeling uncertainty Combinations of the above Discuss all three briefly The first one: Brockett’s necessary condition One way out - hybrid feedback

PARKING PROBLEM Nonholonomic constraint: wheels do not slip Explain the equations Explain the constraint This is controllable nonholonomic: can move anywhere eventually, but there are constraints on where can move instantaneously Parking problem is not solvable with continuous feedback Nonholonomic constraint: wheels do not slip

OBSTRUCTION to STABILIZATION ? Draw arrows to explain the singularity Can move away from the line for an arbitrary time This is not just discontinuous feedback: there are two different modes of operation. Discrete state variable Put back the “Reasons” slide Solution: move away first