cvxSetOpt
computes an updated candidate terminal region and the corresponding safety-preserving controller.
Contents
Syntax
[res, opts] = cvxSetOpt(res, opts, enlarge)
Description
This function computes the ingredients for, solves, and post-processes the solution of the convex programming approximation for the computation of a robust control invariant (RCI) set for a nonlinear sampled-data system.
Input Arguments
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candTermReg
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current candidate for the terminal region
(class: zonotope)
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opts
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structure containing the algorithm settings
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.X
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set of admissible states (class: interval)
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.U
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set of admissible control inputs
(class: interval)
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.W
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set of disturbances (class: interval)
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.nx
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dimension of state space
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.nu
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dimension of input space
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.nw
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dimension of disturbance space
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.Ninter
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number of intermediate time steps
[{1} / positive integer]
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.timeStep
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sampling time [{0.1} / positive scalar]
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.timeStepCtrl
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sampling time for the control inputs
[-.timeStep/-.Ninter]
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.xEq
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equilibrium point for the terminal region
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.uEq
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control input for the equilirium point
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.trustRegionAlg
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structure containing the trust region and
parameters for updating the trust region
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.scvx
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parameters for successive convexification
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.sys
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structure containing the nonlinearSys
object modeling the dynmical system
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.linDyn
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strucutre containing the matrices of the
linearized dynamical system
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enlarge
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enlargement factor for abstraction error -
optional argument (class: double)
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Output Arguments
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res
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structure containing the results of the last iteration
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.termReg
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updated candidate terminal Region
(class: zonotope)
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.inputFF
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sets representing the safety-preserving
controller associated with -.termReg
(cell array of zonotopes)
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.assignInput
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maps generators of -.inputFF to generators
of -.termReg (cell array of double arrays)
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.flag
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indicates feasibility of the solution of
convex program (class: boolean)
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.time.cvx
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(approx. of) solver time
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.time.cvxSetup
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elasped time for setting up the convex
program in standard form
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.cost.set
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set whose volume is was maximized
(-.termReg or inscribed set)
(class: zonotope)
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.linReach.Rtp
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approximation of the time-point reachable
set, see [1] (class: zonotope)
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.linReach.Rti
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approximation of the time-interval
reachable set, see [1] (class: zonotope)
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opts
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updated opts structure - updated fields:
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.trustRegionAlg.trustRegion
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updated trust region
(class: zonotope)
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See also
terminalRegion, termRegNonlinSysLinApproach
References
[1] L. Schäfer et al. "Scalable Computation of Robust Control Invariant Sets of Nonlinear Systems", 2023, IEEE Transactions on Automatic Control [2] M. Althoff et al. "Reachability Analysis of Nonlinear Systems with Uncertain Parameters using Conservative Linearization", 2008 47th IEEE Conference on Decision and Control, 2008, pp. 4042-4048
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