stoch_mpc_slides

# stoch_mpc_slides - Stochastic Model Predictive Control...

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Stochastic Model Predictive Control stochastic finite horizon control stochastic dynamic programming certainty equivalent model predictive control Prof. S. Boyd, EE364b, Stanford University

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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 0 ,...,x t ) is the state history up to time t causal state-feedback control: u t = φ t ( X t ) = ψ t ( x 0 ,w 0 ,...,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 0 ,w 0 ,...,w T - 1 ) is a random variable objective: J = E parenleftBig T - 1 t =0 t ( x t ,u t ) + T ( x T ) parenrightBig convex stage cost functions t : R n × R m R , t = 0 ,...,T 1 convex terminal cost function T : R n R J depends on control policies φ 0 ,...,φ T - 1 constraints: u t ∈ U t , t = 0 ,...,T 1 convex input constraint sets U 0 ,..., U T - 1 stochastic control problem: choose control policies φ 0 ,...,φ T - 1 to minimize J , subject to constraints Prof. S. Boyd, EE364b, Stanford University 2

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Stochastic finite horizon control an infinite dimensional problem: variables are functions φ 0 ,...,φ T - 1 can restrict policies to finite dimensional subspace, e.g. , φ t all affine key idea: we have recourse (a.k.a. feedback, closed-loop control)
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