compTermRegSubpaving
compute terminal region with subpaving algorithm
Contents
Syntax
T = compTermRegSubpaving(benchmark,Param,Opts)
Description
This function first computes a terminal controller that stabilizes the system around the specified equilibrium point using a Linear Quadratic Regulator, and then computes a terminal region for the contolled system with the subpaving algorithm in [1].
Input Arguments
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benchmark
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name of the considered benchmark model (see;
"aroc/benchmarks/dynamics/...")
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Param
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a structure containing the benchmark parameters
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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 uncertain disturbances (class: interval;
or zonotope)
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.V
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set of measurement errors (class: interval or;
zonotope)
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.X
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set of state constraints (class: mptPolytope)
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Opts
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a structure containing the algorithm settings
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.Tdomain
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search domain for the terminal region (class:;
interval)
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.Tinit
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initial guess for the terminal region (class:;
interval)
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.xEq
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states for the equibrium point of the system
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.uEq
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control inputs for the equilibrium point of the
system
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.K
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feedback matrix for the terminal contorller
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.Q
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state weighting matrix for the LQR approach
applied to determine the terminal controller
[{eye(nx)} / positive-definite square matrix]
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.R
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input weighting matrix for the LQR approach
applied to determine the terminal controller
[{zeros(nu)} / positive-definite square matrix]
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.numRef
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number of refinement steps for the box size
[{4}, positive integer]
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.tMax
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final time for reachability analysis
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.reachSteps
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number of reachability steps in one time step
[{20} / positive integer]
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.enlargeFac
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enlargement factor for enlargin the initial
guess Opts.Tinit
[{1.5}, double > 1]
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.cora.alg
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reachability algorithm that is used
('lin' or 'poly')
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.cora.tensorOrder
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taylor order for the abstraction of
the nonlinear function (2 or 3)
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.cora.taylorTerms
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taylor order for computing e^At
[{10} / positive integer]
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.cora.zonotopeOrder
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upper bound for the zonotope order
[{50} / positive integer]
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.cora.errorOrder
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upper bound for the zonotope order
before comp. the abstraction error
[{5} / positive integer]
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.cora.intermediateOrder
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upper bound for the zonotope order
during internal computations
[{50} / positive integer]
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Output Arguments
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T
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object of class termRegSubpaving
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See Also
terminalRegion, termRegSubpaving
References
- [1] El-Guindy et al. (2017), Estimating the region of attraction via forward reachable sets, ACC 2017
© 2018-2023 I6 Technische Universität München
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