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med02-workshop-Daniel (1)

# med02-workshop-Daniel (1) - TUTORIAL on LOGIC-BASED CONTROL...

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TUTORIAL on LOGIC-BASED CONTROL Part I: SWITCHED CONTROL SYSTEMS Daniel Liberzon Coordinated Science Laboratory and Dept. of Electrical & Computer Eng., Univ. of Illinois at Urbana-Champaign MED ’02, Lisbon

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OUTLINE Switched Control Systems Stability of Switched Systems Questions, Break
OUTLINE Switched Control Systems Stability of Switched Systems Questions, Break

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SWITCHED and HYBRID SYSTEMS Switching can be: State-dependent or Time-dependent Hybrid systems: interaction of continuous and discrete dynamics Switched systems: continuous systems with discrete switchings emphasis on properties of continuous state ) ( x f x σ = and is a switching signal P ) , 0 [ : σ where is a family of systems P p x f x p = ), ( Autonomous or Controlled
SWITCHING CONTROL Classical continuous feedback paradigm: u y P C u y P Plant: But logical decisions are often necessary: The closed-loop system is hybrid u y C 1 C 2 l o g i c P

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REASONS for SWITCHING Nature of the control problem Sensor or actuator limitations Large modeling uncertainty Combinations of the above
REASONS for SWITCHING Nature of the control problem Sensor or actuator limitations Large modeling uncertainty Combinations of the above

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PARKING PROBLEM 2 x 1 x φ cos 1 1 w x = φ sin 1 2 w x = 2 w = φ Nonholonomic constraint: wheels do not slip φ
OBSTRUCTION to STABILIZATION Solution: move away first ?

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REASONS for SWITCHING Nature of the control problem Sensor or actuator limitations Large modeling uncertainty Combinations of the above
OUTPUT FEEDBACK switched system Example : harmonic oscillator y u - = y u 2 1 = u y y = +

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QUANTIZED FEEDBACK PLANT QUANTIZER CONTROLLER u x q(x) x q(x) sensitivity M values
OBSTRUCTION to STABILIZATION Assume: fixed , M Asymptotic stabilization is impossible

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MOTIVATING EXAMPLES 1. Temperature sensor normal too low too high 2. Camera with zoom Tracking a golf ball 3. Coding and decoding
VARYING the SENSITIVITY zoom out zoom in Why switch ?

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med02-workshop-Daniel (1) - TUTORIAL on LOGIC-BASED CONTROL...

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