383 research outputs found
On control of discrete-time state-dependent jump linear systems with probabilistic constraints: A receding horizon approach
In this article, we consider a receding horizon control of discrete-time
state-dependent jump linear systems, particular kind of stochastic switching
systems, subject to possibly unbounded random disturbances and probabilistic
state constraints. Due to a nature of the dynamical system and the constraints,
we consider a one-step receding horizon. Using inverse cumulative distribution
function, we convert the probabilistic state constraints to deterministic
constraints, and obtain a tractable deterministic receding horizon control
problem. We consider the receding control law to have a linear state-feedback
and an admissible offset term. We ensure mean square boundedness of the state
variable via solving linear matrix inequalities off-line, and solve the
receding horizon control problem on-line with control offset terms. We
illustrate the overall approach applied on a macroeconomic system
Stability for Receding-horizon Stochastic Model Predictive Control
A stochastic model predictive control (SMPC) approach is presented for
discrete-time linear systems with arbitrary time-invariant probabilistic
uncertainties and additive Gaussian process noise. Closed-loop stability of the
SMPC approach is established by appropriate selection of the cost function.
Polynomial chaos is used for uncertainty propagation through system dynamics.
The performance of the SMPC approach is demonstrated using the Van de Vusse
reactions.Comment: American Control Conference (ACC) 201
Stochastic model predictive control for constrained networked control systems with random time delay
In this paper the continuous time stochastic constrained optimal control problem is formulated for the class of networked control systems assuming that time delays follow a discrete-time, finite Markov chain . Polytopic overapproximations of the system's trajectories are employed to produce a polyhedral inner approximation of the non-convex constraint set resulting from imposing the constraints in continuous time. The problem is cast in a Markov jump linear systems (MJLS) framework and a stochastic MPC controller is calculated explicitly, oine, coupling dynamic programming with parametric piecewise quadratic (PWQ) optimization. The calculated control law leads to stochastic stability of the closed loop system, in the mean square sense and respects the state and input constraints in continuous time
Second moment constraints and the control problem of Markov jump linear systems
This paper addresses the optimal solution for the regulator control problem of Markov jump linear systems subject to second moment constraints. We can characterize and obtain the solution explicitly using linear matrix inequalities techniques. The constraints are imposed on the second moment of both the system state and control vector, and the optimal solution is obtained in a computable form. To illustrate the usefulness of the approach, specially that for systems subject to abrupt variations and physical limitations, we present an application for one joint of the European Robotic Arm
Stability for Receding-horizon Stochastic Model Predictive Control
A stochastic model predictive control (SMPC) approach is presented for
discrete-time linear systems with arbitrary time-invariant probabilistic
uncertainties and additive Gaussian process noise. Closed-loop stability of the
SMPC approach is established by appropriate selection of the cost function.
Polynomial chaos is used for uncertainty propagation through system dynamics.
The performance of the SMPC approach is demonstrated using the Van de Vusse
reactions.Comment: American Control Conference (ACC) 201
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