105 research outputs found
Min-max model predictive control as a quadratic program
This paper deals with the implementation of min-max model predictive control for constrained linear systems with bounded additive uncertainties and quadratic cost functions. This type of controller has been shown to be a continuous piecewise affine function of the state vector by geometrical methods. However, no algorithm for computing the explicit solution has been given. In this paper, we show that the min-max optimization problem can be expressed as a multi-parametric quadratic program, and so, the explicit form of the controller may be determined by standard multi-parametric techniques
Three Essays on Decision Making under Uncertainty in Electric Power Systems
This thesis consists of three essays, discussing three different but connected problems on decision making under uncertainty in electricpower systems.The first essay uses a system model to examine how various factors affect the market price of electricity, and decomposes the price toquantitatively evaluate the contributions of individual factors as well as their interactions. Sensitivity analysis results from a parametric quadratic program are applied in the computation.The second essay formulates the well studied security constrained economic dispatch (SCED) problem as a Markov decision process model,where the action space is a polyhedron defined by linear generation and transmission constraints. Such a model enables the decision maker to accurately evaluate the impact of a dispatch decision to the entire future operation of the electric power system.The third essay examines the effect of demand and supply side uncertainties on the exercise of market power. Solutions under Bertrand, Cournot, and linear supply function equilibrium (LSFE)models are derived and compared.The three problems studied in the essays are a unique representation of different levels of the decision making process in a sophisticated deregulated electric power system, using techniques from both mathematical programming and probability/statistics
Strong Stationarity Conditions for Optimal Control of Hybrid Systems
We present necessary and sufficient optimality conditions for finite time
optimal control problems for a class of hybrid systems described by linear
complementarity models. Although these optimal control problems are difficult
in general due to the presence of complementarity constraints, we provide a set
of structural assumptions ensuring that the tangent cone of the constraints
possesses geometric regularity properties. These imply that the classical
Karush-Kuhn-Tucker conditions of nonlinear programming theory are both
necessary and sufficient for local optimality, which is not the case for
general mathematical programs with complementarity constraints. We also present
sufficient conditions for global optimality.
We proceed to show that the dynamics of every continuous piecewise affine
system can be written as the optimizer of a mathematical program which results
in a linear complementarity model satisfying our structural assumptions. Hence,
our stationarity results apply to a large class of hybrid systems with
piecewise affine dynamics. We present simulation results showing the
substantial benefits possible from using a nonlinear programming approach to
the optimal control problem with complementarity constraints instead of a more
traditional mixed-integer formulation.Comment: 30 pages, 4 figure
Learning an Approximate Model Predictive Controller with Guarantees
A supervised learning framework is proposed to approximate a model predictive
controller (MPC) with reduced computational complexity and guarantees on
stability and constraint satisfaction. The framework can be used for a wide
class of nonlinear systems. Any standard supervised learning technique (e.g.
neural networks) can be employed to approximate the MPC from samples. In order
to obtain closed-loop guarantees for the learned MPC, a robust MPC design is
combined with statistical learning bounds. The MPC design ensures robustness to
inaccurate inputs within given bounds, and Hoeffding's Inequality is used to
validate that the learned MPC satisfies these bounds with high confidence. The
result is a closed-loop statistical guarantee on stability and constraint
satisfaction for the learned MPC. The proposed learning-based MPC framework is
illustrated on a nonlinear benchmark problem, for which we learn a neural
network controller with guarantees.Comment: 6 pages, 3 figures, to appear in IEEE Control Systems Letter
An Extended Kalman Filter for Data-enabled Predictive Control
The literature dealing with data-driven analysis and control problems has
significantly grown in the recent years. Most of the recent literature deals
with linear time-invariant systems in which the uncertainty (if any) is assumed
to be deterministic and bounded; relatively little attention has been devoted
to stochastic linear time-invariant systems. As a first step in this direction,
we propose to equip the recently introduced Data-enabled Predictive Control
algorithm with a data-based Extended Kalman Filter to make use of additional
available input-output data for reducing the effect of noise, without
increasing the computational load of the optimization procedure
- …