stoch_mpc_slides - Stochastic Model Predictive Control •...

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Unformatted text preview: Stochastic Model Predictive Control • stochastic finite horizon control • stochastic dynamic programming • certainty equivalent model predictive control Prof. S. Boyd, EE364b, Stanford University Causal state-feedback control • linear dynamical system, over finite time horizon: x t +1 = Ax t + Bu t + w t , t = 0 ,...,T − 1 – x t ∈ R n is state, u t ∈ R m is the input at time t – w t is the process noise (or exogeneous input) at time t • X t = ( x ,...,x t ) is the state history up to time t • causal state-feedback control: u t = φ t ( X t ) = ψ t ( x ,w ,...,w t- 1 ) , t = 0 ,...,T − 1 • φ t : R ( t +1) n → R m called the control policy at time t Prof. S. Boyd, EE364b, Stanford University 1 Stochastic finite horizon control • ( x ,w ,...,w T- 1 ) is a random variable • objective: J = E parenleftBig ∑ T- 1 t =0 ℓ t ( x t ,u t ) + ℓ T ( x T ) parenrightBig – convex stage cost functions ℓ t : R n × R m → R , t = 0 ,...,T − 1 – convex terminal cost function ℓ T : R n → R • J depends on control policies φ ,...,φ T- 1 • constraints: u t ∈ U t , t = 0 ,...,T − 1 – convex input constraint sets U ,..., U T- 1 • stochastic control problem: choose control policies φ ,...,φ T- 1 to minimize J , subject to constraints Prof. S. Boyd, EE364b, Stanford University 2 Stochastic finite horizon control • an infinite dimensional problem: variables are functions φ ,...,φ T- 1 – can restrict policies to finite dimensional subspace,...
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stoch_mpc_slides - Stochastic Model Predictive Control •...

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