159,871 research outputs found
Learning the cost-to-go for mixed-integer nonlinear model predictive control
Application of nonlinear model predictive control (NMPC) to problems with
hybrid dynamical systems, disjoint constraints, or discrete controls often
results in mixed-integer formulations with both continuous and discrete
decision variables. However, solving mixed-integer nonlinear programming
problems (MINLP) in real-time is challenging, which can be a limiting factor in
many applications. To address the computational complexity of solving mixed
integer nonlinear model predictive control problem in real-time, this paper
proposes an approximate mixed integer NMPC formulation based on value function
approximation. Leveraging Bellman's principle of optimality, the key idea here
is to divide the prediction horizon into two parts, where the optimal value
function of the latter part of the prediction horizon is approximated offline
using expert demonstrations. Doing so allows us to solve the MINMPC problem
with a considerably shorter prediction horizon online, thereby reducing the
online computation cost. The paper uses an inverted pendulum example with
discrete controls to illustrate this approach
Online-Computation Approach to Optimal Control of Noise-Affected Nonlinear Systems with Continuous State and Control Spaces
© 2007 EUCA.A novel online-computation approach to optimal control of nonlinear, noise-affected systems with continuous state and control spaces is presented. In the proposed algorithm, system noise is explicitly incorporated into the control decision. This leads to superior results compared to state-of-the-art nonlinear controllers that neglect this influence. The solution of an optimal nonlinear controller for a corresponding deterministic system is employed to find a meaningful state space restriction. This restriction is obtained by means of approximate state prediction using the noisy system equation. Within this constrained state space, an optimal closed-loop solution for a finite decision-making horizon (prediction horizon) is determined within an adaptively restricted optimization space. Interleaving stochastic dynamic programming and value function approximation yields a solution to the considered optimal control problem. The enhanced performance of the proposed discrete-time controller is illustrated by means of a scalar example system. Nonlinear model predictive control is applied to address approximate treatment of infinite-horizon problems by the finite-horizon controller
Reliable autonomous vehicle control - a chance constrained stochastic MPC approach
In recent years, there is a growing interest in the development of systems capable of performing
tasks with a high level of autonomy without human supervision. This kind of systems are known as
autonomous systems and have been studied in many industrial applications such as automotive,
aerospace and industries. Autonomous vehicle have gained a lot of interest in recent years and have
been considered as a viable solution to minimize the number of road accidents. Due to the
complexity of dynamic calculation and the physical restrictions in autonomous vehicle, for example,
deterministic model predictive control is an attractive control technique to solve the problem of
path planning and obstacle avoidance. However, an autonomous vehicle should be capable of driving
adaptively facing deterministic and stochastic events on the road. Therefore, control design for
the safe, reliable and autonomous driving should consider vehicle model uncertainty as well
uncertain external influences. The stochastic model predictive control scheme provides the
most convenient scheme for the control of autonomous vehicles on moving horizons, where chance
constraints are to be used to guarantee the reliable fulfillment of trajectory constraints and
safety against static and random obstacles. To solve this kind of problems is known as chance
constrained model predictive control. Thus, requires the solution of a chance constrained
optimization on moving horizon. According to the literature, the major challenge for solving chance
constrained optimization is to calculate the value of probability. As a result, approximation
methods have been proposed for solving this task.
In the present thesis, the chance constrained optimization for the autonomous vehicle is solved
through approximation method, where the probability constraint is approximated by using a smooth
parametric function. This methodology presents two approaches that allow the solution of chance
constrained optimization problems in inner approximation and outer approximation. The aim of this
approximation methods is to reformulate the chance constrained optimizations problems as a sequence
of nonlinear programs. Finally, three case studies of autonomous vehicle for tracking and obstacle
avoidance are presented in this work, in which three levels probability of reliability are
considered
for the optimal solution.Tesi
Approximate solution of stochastic infinite horizon optimal control problems for constrained linear uncertain systems
We propose a Model Predictive Control (MPC) with a single-step prediction
horizon to solve infinite horizon optimal control problems with the expected
sum of convex stage costs for constrained linear uncertain systems. The
proposed method relies on two techniques. First, we estimate the expected
values of the convex costs using a computationally tractable approximation,
achieved by sampling across the space of disturbances. Second, we implement a
data-driven approach to approximate the optimal value function and its
corresponding domain, through systematic exploration of the system's state
space. These estimates are subsequently used as the terminal cost and terminal
set within the proposed MPC. We prove recursive feasibility, robust constraint
satisfaction, and convergence in probability to the target set. Furthermore, we
prove that the estimated value function converges to the optimal value function
in a local region. The effectiveness of the proposed MPC is illustrated with
detailed numerical simulations and comparisons with a value iteration method
and a Learning MPC that minimizes a certainty equivalent cost.Comment: Submitted to the IEEE Transactions on Automatic Contro
Online-Computation Approach to Optimal Control of Noise-Affected Nonlinear Systems with Continuous State and Control Spaces
A novel online-computation approach to optimal control of nonlinear, noise-affected systems with continuous state and control spaces is presented. In the proposed algorithm, system noise is explicitly incorporated into the control decision. This leads to superior results compared to state-of-the-art nonlinear controllers that neglect this influence. The solution of an optimal nonlinear controller for a corresponding deterministic system is employed to find a meaningful state space restriction. This restriction is obtained by means of approximate state prediction using the noisy system equation. Within this constrained state space, an optimal closed-loop solution for a finite decisionmaking horizon (prediction horizon) is determined within an adaptively restricted optimization space. Interleaving stochastic dynamic programming and value function approximation yields a solution to the considered optimal control problem. The enhanced performance of the proposed discrete-time controller is illustrated by means of a scalar example system. Nonlinear model predictive control is applied to address approximate treatment of infinite-horizon problems by the finite-horizon controller
Approximate Dynamic Programming for Constrained Piecewise Affine Systems with Stability and Safety Guarantees
Infinite-horizon optimal control of constrained piecewise affine (PWA)
systems has been approximately addressed by hybrid model predictive control
(MPC), which, however, has computational limitations, both in offline design
and online implementation. In this paper, we consider an alternative approach
based on approximate dynamic programming (ADP), an important class of methods
in reinforcement learning. We accommodate non-convex union-of-polyhedra state
constraints and linear input constraints into ADP by designing PWA penalty
functions. PWA function approximation is used, which allows for a mixed-integer
encoding to implement ADP. The main advantage of the proposed ADP method is its
online computational efficiency. Particularly, we propose two control policies,
which lead to solving a smaller-scale mixed-integer linear program than
conventional hybrid MPC, or a single convex quadratic program, depending on
whether the policy is implicitly determined online or explicitly computed
offline. We characterize the stability and safety properties of the closed-loop
systems, as well as the sub-optimality of the proposed policies, by quantifying
the approximation errors of value functions and policies. We also develop an
offline mixed-integer linear programming-based method to certify the
reliability of the proposed method. Simulation results on an inverted pendulum
with elastic walls and on an adaptive cruise control problem validate the
control performance in terms of constraint satisfaction and CPU time
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