Prezentácia programu PowerPointoravec/mup/files/support/how2... · RMPC Approaches Kothare et al....

How2use mup

J. Oravec – M. Bakošová

2016-05-23

R20160321

Disclaimer% Copyright is with the following author(s):%% (c) 2016 Juraj Oravec, Slovak University of Technology in Bratislava,% juraj.oravec@stuba.sk% (c) 2016 Monika Bakosova, Slovak University of Technology in Bratislava,% monika.bakosova@stuba.sk% -----------------------------------------------------------------------------------------------

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Disclaimer% Legal note:% This program is free software; you can redistribute it and/or% modify it under the terms of the GNU General Public% License as published by the Free Software Foundation; either% version 2.1 of the License, or (at your option) any later version.%% This program is distributed in the hope that it will be useful,% but WITHOUT ANY WARRANTY; without even the implied warranty of% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU% General Public License for more details.%% You should have received a copy of the GNU General Public% License along with this library; if not, write to the% Free Software Foundation, Inc.,% 59 Temple Place, Suite 330,% Boston, MA 02111-1307 USA

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Problems to solve

RMPC

System

u(k) x(k)q(k)

Problems to solve

RMPC

System

u(k) x(k)q(k)

Problems to solve

RMPC

System

u(k) x(k)q(k)

Problems to solve

RMPC

System

u(k) x(k)q(k)

Problems to solve

RMPC

System

u(k) x(k)q(k)

RMPC

System

u(k) x(k)q(k)

Problems to solve

SDP:

RMPC

System

u(k) x(k)q(k)

Problems to solve

Control law:

RMPC

System

u(k) x(k)q(k)

Problems to solve

Control law:

Quality criterion:

Framework

System

u(k)

SDPFeas. Check

Control Law

SDP Solver

YALMIP

advanced analysis

feas.

infeas.

mup

x(k)

Framework

System

u(k)

SDPFeas. Check

Control Law

SDP Solver

YALMIP

advanced analysis

feas.

infeas.

mup

x(k)

Framework

System

u(k)

SDPFeas. Check

Control Law

SDP Solver

YALMIP

advanced analysis

feas.

infeas.

mup

x(k)

Framework

System

u(k)

SDPFeas. Check

Control Law

SDP Solver

YALMIP

advanced analysis

feas.

infeas.

mup

x(k)

Framework

System

u(k)

SDPFeas. Check

Control Law

SDP Solver

YALMIP

advanced analysis

feas.

infeas.

mup

x(k)

Framework

System

u(k)

SDPFeas. Check

Control Law

SDP Solver

YALMIP

advanced analysis

feas.

infeas.

mup

x(k)

Framework

System

u(k)

SDPFeas. Check

Control Law

SDP Solver

YALMIP

advanced analysis

feas.

infeas.

mup

x(k)

Framework

System

u(k)

SDPFeas. Check

Control Law

SDP Solver

YALMIP

advanced analysis

feas.

infeas.

mup

x(k)

Framework

System

u(k)

SDPFeas. Check

Control Law

SDP Solver

YALMIP

advanced analysis

feas.

infeas.

mup

x(k)

Framework

System

u(k)

SDPFeas. Check

Control Law

SDP Solver

YALMIP

advanced analysis

feas.

infeas.

mup

x(k)

MATLAB Compatibility

r2013a

mup

r2014br2013a

mup

OpenGL

MATLAB Compatibility

r2014br2013a

mup

r2012a

OpenGL.slx

MATLAB Compatibility

r2014br2013a

mup

r2012ar2011b

OpenGL.slx.mdl

MATLAB Compatibility

r2014br2013a

mup

r2012ar2011b

OpenGL.slx.mdl

MATLAB Compatibility

• MATLAB/Simulink: rmpc_block (beginner)

• MATLAB: CLI (advanced)

How to use it ?

• MATLAB/Simulink: rmpc_block (beginner)

• MATLAB: CLI (advanced)

How to use it ?

LQR

System

u(k) x(k)

Simulink Block

u(k)x(k)

LQR

-K-

System

u(k) x(k)

x(k) u(k)

Simulink Block

bitbucket.org/oravec/mup

Simulink Block

RMPC

System

u(k) x(k)

rmpc_block

inputscost

feasibility

controllergamma

states

solver_timecounter

x(k) u(k)

inputs

cost

feasibility

controller

gamma

states

rmpc_block

solver_time

counter

inputs

cost

feasibility

controller

gamma

states

rmpc_block

solver_time

counter

x(k)

inputs

cost

feasibility

controller

gamma

states

rmpc_block

solver_time

counter

x(k)

inputs

cost

feasibility

controller

gamma

states

rmpc_block

solver_time

counter

x(k)

u(k)

Control law:

inputs

cost

feasibility

controller

gamma

states

rmpc_block

solver_time

counter

x(k)

u(k)

J(k)

inputs

cost

feasibility

controller

gamma

states

rmpc_block

solver_time

counter

x(k)

u(k)

J(k)

c(k)

inputs

cost

feasibility

controller

gamma

states

rmpc_block

solver_time

counter

x(k)

u(k)

J(k)

c(k)

F(k)

Control law:

inputs

cost

feasibility

controller

gamma

states

rmpc_block

solver_time

counter

x(k)

u(k)

J(k)

c(k)

γ

F(k)

SDP:

inputs

cost

feasibility

controller

gamma

states

rmpc_block

solver_time

counter

x(k)

u(k)

J(k)

c(k)

γ

F(k)

tsol

inputs

cost

feasibility

controller

gamma

states

rmpc_block

solver_time

counter

x(k)

u(k)

J(k)

c(k)

γ

F(k)

k

tsol

x(k)

u(k)

J(k)

c(k)

γ

F(k)

k

tsol

inputs

cost

feasibility

controller

gamma

states

rmpc_block

solver_time

counter

RMPC Configuration

RMPC Approaches

RMPC ApproachesKothare et al. (1996) Cuzzola et al. (2002) Mao (2003)Wan et al. (2003)Ding et al. (2007)Li et al. (2008) Cao et Li (2005)Huang et al. (2011)Zhang et al. (2013)

RMPC ApproachesKothare et al. (1996) Cuzzola et al. (2002) Mao (2003)Wan et al. (2003)Ding et al. (2007)Li et al. (2008) Cao et Li (2005)Huang et al. (2011)Zhang et al. (2013)NSO and ACISNSO and WACISNSO and SDLFPDLF and ACISPDLF and WACIS

RMPC ApproachesKothare et al. (1996) Cuzzola et al. (2002) Mao (2003)Wan et al. (2003)Ding et al. (2007)Li et al. (2008) Cao et Li (2005)Huang et al. (2011)Zhang et al. (2013)NSO and ACISNSO and WACISNSO and SDLFPDLF and ACISPDLF and WACISKothare et al. (1996) – Soft-ConWan et al. (2003) – Soft-ConCao et Li (2005) – Soft-ConNSO and ACIS – Soft-Con

Opt. Problem Design

• initial:speed up

• reformulation:analysis

Opt. Problem Design

• default:

• SDP:

Feasibility Tolerance

Uncertain System

Uncertain System

Uncertain System

Quality criterion

Quality criterion

Parameters

optional RMPC design and tuning parameters

Soft Constraints

Soft Constraints

enable

Soft Constraints

Soft Constraints

Setup

SDP Solver

SDP Solver

• CSDP (free)• DSDP (free)• LMILAB (comercial)• LOGDETPPA (free)• MOSEK (free for academia)• PENBMI (comercial)• PENLAB (free)• PENSDP (free for academia)• SDPA (free)• SDPLR (free)• SDPT3 (free)• SDPNAL (free)• SEDUMI (free)

users.isy.liu.se/johanl/yalmip/pmwiki.php?n=Solvers.Solvers

Verbose Mode

• Normal• Silent• Loud (recommended)

Verbose Mode

YALMIP Verbose Mode

• Silent• Loud

YALMIP Verbose Mode

• MATLAB/Simulink: rmpc_block (beginner)

• MATLAB: CLI (advanced)

How to use it ?

%% System

A{1}=...; A{2}=...; A{3}=...; A{4}=...;

B{1}=...; B{2}=...; B{3}=...; B{4}=...;

C{1}=...; C{2}=...; C{3}=...; C{4}=...;

ts=0.5; % Sampling Time

x0=...; % Initial Conditions

1:

2:

3:

4:

5:

6:

CLI

%% System

A{1}=...; A{2}=...; A{3}=...; A{4}=...;

B{1}=...; B{2}=...; B{3}=...; B{4}=...;

C{1}=...; C{2}=...; C{3}=...; C{4}=...;

ts=0.5; % Sampling Time

x0=...; % Initial Conditions

1:

2:

3:

4:

5:

6:

CLI

%% System

A{1}=...; A{2}=...; A{3}=...; A{4}=...;

B{1}=...; B{2}=...; B{3}=...; B{4}=...;

C{1}=...; C{2}=...; C{3}=...; C{4}=...;

ts=0.5; % Sampling Time

x0=...; % Initial Conditions

1:

2:

3:

4:

5:

6:

CLI

%% Symmetric constraints

u_max=...; % Input constraints

x_max=...; % State constraints

1:

2:

3:

CLI

%% Symmetric constraints

u_max=...; % Input constraints

x_max=...; % State constraints

1:

2:

3:

CLI

%% RMPC design

Wx=...; Wu=...; % Weight matrices

[method,kwd] = mup_cli_rmpc_method; % Method

mup_sdp % SDP formulation

mup_rmpc_opt % RMPC design

1:

2:

3:

4:

5:

CLI

%% RMPC design

Wx=...; Wu=...; % Weight matrices

[method,kwd] = mup_cli_rmpc_method; % Method

mup_sdp % SDP formulation

mup_rmpc_opt % RMPC design

1:

2:

3:

4:

5:

CLI

%% RMPC design

Wx=...; Wu=...; % Weight matrices

[method,kwd] = mup_cli_rmpc_method; % Method

mup_sdp % SDP formulation

mup_rmpc_opt % RMPC design

1:

2:

3:

4:

5:

CLI

%% RMPC design

Wx=...; Wu=...; % Weight matrices

[method,kwd] = mup_cli_rmpc_method; % Method

mup_sdp % SDP formulation

mup_rmpc_opt % RMPC design

1:

2:

3:

4:

5:

CLI

%% RMPC design

Wx=...; Wu=...; % Weight matrices

[method,kwd] = mup_cli_rmpc_method; % Method

mup_sdp % SDP formulation

mup_rmpc_opt % RMPC design

1:

2:

3:

4:

5:

CLI

List of avaliable methods:

1: Cao et al. (2005)

2: Cao et al. (2005) - Soft-Con

3: Cuzzola et al. (2002)

%% RMPC design

Wx=...; Wu=...; % Weight matrices

[method,kwd] = mup_cli_rmpc_method; % Method

mup_sdp % SDP formulation

mup_rmpc_opt % RMPC design

1:

2:

3:

4:

5:

CLI

%% RMPC design

Wx=...; Wu=...; % Weight matrices

[method,kwd] = mup_cli_rmpc_method; % Method

mup_sdp % SDP formulation

mup_rmpc_opt % RMPC design

1:

2:

3:

4:

5:

CLI

%% Closed-loop control in k-th step

u = mup_rmpc{x,design}; % RMPC control law

1:

2:

CLI

%% Closed-loop control in k-th step

u = mup_rmpc{x,design}; % RMPC control law

1:

2:

CLI

%% Closed-loop control in k-th step

u = mup_rmpc{x,design}; % RMPC control law

1:

2:

CLI

Feasibility Check

Feasibility Check

enable

• Normal• Silent• Loud (recommended)

Verbose Mode

Feasibility Check /Normal MUP:BLOCK:RMPC: FEASIBILITY_CHECK initialized...MUP:BLOCK:RMPC: Valid. (0.12)MUP:BLOCK:RMPC: FEASIBILITY_CHECK: Termined. (0.03 sec)

2.5 GHz CPU, 4GB RAM, MATLAB 2013a, MOSEK

Feasibility Check /Normal MUP:BLOCK:RMPC: FEASIBILITY_CHECK initialized...MUP:BLOCK:RMPC: Valid. (0.12)MUP:BLOCK:RMPC: FEASIBILITY_CHECK: Termined. (0.03 sec)

2.5 GHz CPU, 4GB RAM, MATLAB 2013a, MOSEK

Feasibility Check /Normal MUP:BLOCK:RMPC: FEASIBILITY_CHECK initialized...FEAS_CHK: VTX:2|I:1: Stability condition violated!FEAS_CHK: VTX:2|I:2: Stability condition violated!FEAS_CHK: VTX:1|I:1: State contraints violated!FEAS_CHK: VTX:1|I:2: State contraints violated!FEAS_CHK: VTX:2|I:1: State contraints violated!FEAS_CHK: VTX:2|I:2: State contraints violated!FEAS_CHK: VTX:3|I:1: State contraints violated!FEAS_CHK: VTX:3|I:2: State contraints violated!FEAS_CHK: Failed! (8 infeasible constraint(s) found) (0.03)MUP:BLOCK:RMPC: Feasibility check failed!MUP:BLOCK:RMPC: Instead of Robust MPC has been designed LQ controllerMUP:BLOCK:RMPC: FEASIBILITY_CHECK: Termined. (0.05 sec)

2.5 GHz CPU, 4GB RAM, MATLAB 2013a, MOSEK

Feasibility Check /Normal MUP:BLOCK:RMPC: FEASIBILITY_CHECK initialized...FEAS_CHK: VTX:2|I:1: Stability condition violated!FEAS_CHK: VTX:2|I:2: Stability condition violated!FEAS_CHK: VTX:1|I:1: State contraints violated!FEAS_CHK: VTX:1|I:2: State contraints violated!FEAS_CHK: VTX:2|I:1: State contraints violated!FEAS_CHK: VTX:2|I:2: State contraints violated!FEAS_CHK: VTX:3|I:1: State contraints violated!FEAS_CHK: VTX:3|I:2: State contraints violated!FEAS_CHK: Failed! (8 infeasible constraint(s) found) (0.03)MUP:BLOCK:RMPC: Feasibility check failed!MUP:BLOCK:RMPC: Instead of Robust MPC has been designed LQ controllerMUP:BLOCK:RMPC: FEASIBILITY_CHECK: Termined. (0.05 sec)

2.5 GHz CPU, 4GB RAM, MATLAB 2013a, MOSEK

Feasibility Check /Normal MUP:BLOCK:RMPC: FEASIBILITY_CHECK initialized...FEAS_CHK: VTX:2|I:1: Stability condition violated!FEAS_CHK: VTX:2|I:2: Stability condition violated!FEAS_CHK: VTX:1|I:1: State contraints violated!FEAS_CHK: VTX:1|I:2: State contraints violated!FEAS_CHK: VTX:2|I:1: State contraints violated!FEAS_CHK: VTX:2|I:2: State contraints violated!FEAS_CHK: VTX:3|I:1: State contraints violated!FEAS_CHK: VTX:3|I:2: State contraints violated!FEAS_CHK: Failed! (8 infeasible constraint(s) found) (0.03)MUP:BLOCK:RMPC: Feasibility check failed!MUP:BLOCK:RMPC: Instead of Robust MPC has been designed LQ controllerMUP:BLOCK:RMPC: FEASIBILITY_CHECK: Termined. (0.05 sec)

2.5 GHz CPU, 4GB RAM, MATLAB 2013a, MOSEK

Feasibility Check /Normal MUP:BLOCK:RMPC: FEASIBILITY_CHECK initialized...FEAS_CHK: VTX:2|I:1: Stability condition violated!FEAS_CHK: VTX:2|I:2: Stability condition violated!FEAS_CHK: VTX:1|I:1: State contraints violated!FEAS_CHK: VTX:1|I:2: State contraints violated!FEAS_CHK: VTX:2|I:1: State contraints violated!FEAS_CHK: VTX:2|I:2: State contraints violated!FEAS_CHK: VTX:3|I:1: State contraints violated!FEAS_CHK: VTX:3|I:2: State contraints violated!FEAS_CHK: Failed! (8 infeasible constraint(s) found) (0.03)MUP:BLOCK:RMPC: Feasibility check failed!MUP:BLOCK:RMPC: Instead of Robust MPC has been designed LQ controllerMUP:BLOCK:RMPC: FEASIBILITY_CHECK: Termined. (0.05 sec)

2.5 GHz CPU, 4GB RAM, MATLAB 2013a, MOSEK

Feasibility Check /Normal MUP:BLOCK:RMPC: FEASIBILITY_CHECK initialized...FEAS_CHK: VTX:2|I:1: Stability condition violated!FEAS_CHK: VTX:2|I:2: Stability condition violated!FEAS_CHK: VTX:1|I:1: State contraints violated!FEAS_CHK: VTX:1|I:2: State contraints violated!FEAS_CHK: VTX:2|I:1: State contraints violated!FEAS_CHK: VTX:2|I:2: State contraints violated!FEAS_CHK: VTX:3|I:1: State contraints violated!FEAS_CHK: VTX:3|I:2: State contraints violated!FEAS_CHK: Failed! (8 infeasible constraint(s) found) (0.03)MUP:BLOCK:RMPC: Feasibility check failed!MUP:BLOCK:RMPC: Instead of Robust MPC has been designed LQ controllerMUP:BLOCK:RMPC: FEASIBILITY_CHECK: Termined. (0.05 sec)

2.5 GHz CPU, 4GB RAM, MATLAB 2013a, MOSEK

Feasibility Check /Normal MUP:BLOCK:RMPC: FEASIBILITY_CHECK initialized...FEAS_CHK: VTX:2|I:1: Stability condition violated!FEAS_CHK: VTX:2|I:2: Stability condition violated!FEAS_CHK: VTX:1|I:1: State contraints violated!FEAS_CHK: VTX:1|I:2: State contraints violated!FEAS_CHK: VTX:2|I:1: State contraints violated!FEAS_CHK: VTX:2|I:2: State contraints violated!FEAS_CHK: VTX:3|I:1: State contraints violated!FEAS_CHK: VTX:3|I:2: State contraints violated!FEAS_CHK: Failed! (8 infeasible constraint(s) found) (0.03)MUP:BLOCK:RMPC: Feasibility check failed!MUP:BLOCK:RMPC: Instead of Robust MPC has been designed LQ controllerMUP:BLOCK:RMPC: FEASIBILITY_CHECK: Termined. (0.05 sec)

2.5 GHz CPU, 4GB RAM, MATLAB 2013a, MOSEK

• Normal• Silent• Loud (recommended)

Verbose Mode

Feasibility Check /LoudFEAS_CHK: Inverse Lyapunov matrix MIN_EIG = 3.275738e+00.FEAS_CHK: I:1: Inverse SDLF matrix W MIN_EIG = 3.115516e-01.FEAS_CHK: I:2: Inverse SDLF matrix W MIN_EIG = 3.115516e-01.FEAS_CHK: I:1: Inverse SDLF matrix Q MIN_EIG = 1.482989e-06.FEAS_CHK: I:2: Inverse SDLF matrix Q MIN_EIG = 1.480064e-06.FEAS_CHK: I:1: Invariant ellipsoid matrix MIN_EIG = 1.566609e-08.FEAS_CHK: I:2: Invariant ellipsoid matrix MIN_EIG = 1.439442e-08.FEAS_CHK: VTX:1|I:1: Stability condition matrix MIN_EIG = 8.704402e-06.FEAS_CHK: VTX:1|I:2: Stability condition matrix MIN_EIG = 8.705740e-06.FEAS_CHK: VTX:2|I:1: Stability condition matrix MIN_EIG = -5.363964e-06.FEAS_CHK: VTX:2|I:1: Stability condition violated!… (shortened)

2.5 GHz CPU, 4GB RAM, MATLAB 2013a, MOSEK

Feasibility Check /LoudFEAS_CHK: Inverse Lyapunov matrix MIN_EIG = 3.275738e+00.FEAS_CHK: I:1: Inverse SDLF matrix W MIN_EIG = 3.115516e-01.FEAS_CHK: I:2: Inverse SDLF matrix W MIN_EIG = 3.115516e-01.FEAS_CHK: I:1: Inverse SDLF matrix Q MIN_EIG = 1.482989e-06.FEAS_CHK: I:2: Inverse SDLF matrix Q MIN_EIG = 1.480064e-06.FEAS_CHK: I:1: Invariant ellipsoid matrix MIN_EIG = 1.566609e-08.FEAS_CHK: I:2: Invariant ellipsoid matrix MIN_EIG = 1.439442e-08.FEAS_CHK: VTX:1|I:1: Stability condition matrix MIN_EIG = 8.704402e-06.FEAS_CHK: VTX:1|I:2: Stability condition matrix MIN_EIG = 8.705740e-06.FEAS_CHK: VTX:2|I:1: Stability condition matrix MIN_EIG = -5.363964e-06.FEAS_CHK: VTX:2|I:1: Stability condition violated!… (shortened)

2.5 GHz CPU, 4GB RAM, MATLAB 2013a, MOSEK

Feasibility Check /LoudFEAS_CHK: Inverse Lyapunov matrix MIN_EIG = 3.275738e+00.FEAS_CHK: I:1: Inverse SDLF matrix W MIN_EIG = 3.115516e-01.FEAS_CHK: I:2: Inverse SDLF matrix W MIN_EIG = 3.115516e-01.FEAS_CHK: I:1: Inverse SDLF matrix Q MIN_EIG = 1.482989e-06.FEAS_CHK: I:2: Inverse SDLF matrix Q MIN_EIG = 1.480064e-06.FEAS_CHK: I:1: Invariant ellipsoid matrix MIN_EIG = 1.566609e-08.FEAS_CHK: I:2: Invariant ellipsoid matrix MIN_EIG = 1.439442e-08.FEAS_CHK: VTX:1|I:1: Stability condition matrix MIN_EIG = 8.704402e-06.FEAS_CHK: VTX:1|I:2: Stability condition matrix MIN_EIG = 8.705740e-06.FEAS_CHK: VTX:2|I:1: Stability condition matrix MIN_EIG = -5.363964e-06.FEAS_CHK: VTX:2|I:1: Stability condition violated!… (shortened)

2.5 GHz CPU, 4GB RAM, MATLAB 2013a, MOSEK

Feasibility Check /LoudFEAS_CHK: Inverse Lyapunov matrix MIN_EIG = 3.275738e+00.FEAS_CHK: I:1: Inverse SDLF matrix W MIN_EIG = 3.115516e-01.FEAS_CHK: I:2: Inverse SDLF matrix W MIN_EIG = 3.115516e-01.FEAS_CHK: I:1: Inverse SDLF matrix Q MIN_EIG = 1.482989e-06.FEAS_CHK: I:2: Inverse SDLF matrix Q MIN_EIG = 1.480064e-06.FEAS_CHK: I:1: Invariant ellipsoid matrix MIN_EIG = 1.566609e-08.FEAS_CHK: I:2: Invariant ellipsoid matrix MIN_EIG = 1.439442e-08.FEAS_CHK: VTX:1|I:1: Stability condition matrix MIN_EIG = 8.704402e-06.FEAS_CHK: VTX:1|I:2: Stability condition matrix MIN_EIG = 8.705740e-06.FEAS_CHK: VTX:2|I:1: Stability condition matrix MIN_EIG = -5.363964e-06.FEAS_CHK: VTX:2|I:1: Stability condition violated!… (shortened)

2.5 GHz CPU, 4GB RAM, MATLAB 2013a, MOSEK