optimalControl

Class prodiving the functionality for solving nonlinear optimal control problems.

Syntax
Description
Input Arguments
Output Arguments
See Also
References

Syntax

obj = optimalControl(system,stageCost,terminalCost,X,U,Q,N,dt)

Description

This class provides the functionality required for solving nonlinear optimal control problems of the form: min sum_k=0^{N-1} l_k(x_k,u_k) + V(x_N), s.t. x0 = x_0, \forall k \in {0,...,N-1}: x_{k+1} = f(x_k,u_k,0), \forall k \in {0,...,N}: x_k \in X, \forall k \in {0,...,N}: u_k \in U, where the stage cost functions l_k(x_k,u_k) might be time-varying, x0 denotes a given initial state, and the sets of admissible states and control inputs X and U, respectively, are assumed to be representable as polytopes. We use IPOPT [1] interfaced via CasADi [2] for solving the optimal control problem.

Input Arguments

system

function handle for the continuous-time dynamics of the controlled system

stageCost

cell array storing function handles for the time-varying stage cost functions (cell array of dimension [N,1])

terminalCost

function handle for the terminal cost function

X

set of admissible states (class: interval / polytope)

U

set of admissible control inputs (class: interval / zonotope)

W

set of disturbances (class: contSet)

N

number of time steps (integer)

dt

sampling time (scalar double)

opts

structure with the following fields

.nw

dimension of the disturbance space (integer)

Output Arguments

obj

generated instance of the class optimalControl

References

[1] A. Wächter and L. T. Biegler, 'On the Implementation of a Primal-Dual Interior Point Filter Line Search Algorithm for Large-Scale Nonlinear Programming', Mathematical Programming 106(1), pp. 25-57, 2006 [2] J. A. E. Andersson et al., 'CasADi – A software framework for nonlinear optimization and optimal control', Mathematical Programming Computation, vol. 11, no. 1, pp. 1–36, 2019.