ECE 555 - Control of Stochastic Systems

Official Description

Stochastic control models; development of control laws by dynamic programming; separation of estimation and control; Kalman filtering; self-tuning regulators; dual controllers; decentralized control. Course Information: Prerequisite: ECE 515 and ECE 534.

Control Systems

Description

Stochastic control models; development of control laws by dynamic programming; separation of estimation and control; Kalman filtering; dual controllers.

Topics

• Introduction: decision-making under uncertainty
• Markov chain models: structure, steady-state probabilities, transience and recurrence, Lyopunov functions and stability
• State space models: state, observation and control processes
• Properties of linear stochastic systems: linear Gaussian systems; asymptotic properties, Gauss-Markov processes; quadratic costs
• Controlled Markov chain models: finite state systems; Markov and stationary policies; cost of Markov policy; infinite state systems
• Input-output models: elimination of state variables; impulse response and frequency response models
• Dynamic programming: optimal control laws; complete and partial information; information state, dual control
• Estimation and control of linear stochastic systems: linear Gaussian systems; Kalman filter; optimal linear-quadradic control; minimum variance control for input-output models
• Identification and adaptive control: Bayesian and non-Bayesian approaches; maximum likelihood estimate; least-squares, prediction error and instrumental variable methods; recursive identification; ODE method; self-tuning regulator

Detailed Description and Outline

Topics:

• Introduction: decision-making under uncertainty
• Markov chain models: structure, steady-state probabilities, transience and recurrence, Lyopunov functions and stability
• State space models: state, observation and control processes
• Properties of linear stochastic systems: linear Gaussian systems; asymptotic properties, Gauss-Markov processes; quadratic costs
• Controlled Markov chain models: finite state systems; Markov and stationary policies; cost of Markov policy; infinite state systems
• Input-output models: elimination of state variables; impulse response and frequency response models
• Dynamic programming: optimal control laws; complete and partial information; information state, dual control
• Estimation and control of linear stochastic systems: linear Gaussian systems; Kalman filter; optimal linear-quadradic control; minimum variance control for input-output models
• Identification and adaptive control: Bayesian and non-Bayesian approaches; maximum likelihood estimate; least-squares, prediction error and instrumental variable methods; recursive identification; ODE method; self-tuning regulator

Texts

P.R. Kumar and P. Varaiya, Stochastic Systems, Prentice-Hall, 1986.

2/13/2013