function varargout = dpm(varargin)
%DPM Dynamic Programming using Matrix operations version 1.1.1
%
% OPTIONS = DPM() returns the standard options structure.
%
% DPM(FUN,NX,NU) saves a random test model with the filename FUN.m
% and NX number of states and NU number of inputs.
%
% [[OUT] DYN] = DPM(FUN,PAR,GRD,PRB,OPTIONS) whith FUN is a function
% handle with the model function. The DPM-function requires that the
% state and input grids are discretized and limited. The function assumes
% equally spaced grids and the GRD structure needed is defined as:
% GRD.X0{.} = 'initial state' (only used in forward simulation)
% GRD.XN{.}.hi = 'final state upper constraint'
% GRD.XN{.}.lo = 'final state lower constraint'
% GRD.Nx{.} = 'number of elements in the state grid'
% GRD.Xn{.}.hi = 'upper boundary of the state grid'
% GRD.Xn{.}.lo = 'lower boundary of the state grid'
% GRD.Nu{.} = 'number of elements in the input grid'
% GRD.Un{.}.hi = 'upper boundary of the input grid'
% GRD.Un{.}.lo = 'lower boundary of the input grid'
% PRB contains the problem parameters
% PRB.Ts = time step
% PRB.N = number of time steps in problem (defines the problem
% length)
% [PRB.N0] = start time index (only used in forward simulation)
% [PRB.W{i}] = (optional) vectors with length PRB.T containing
% disturbances.
% PAR is a user defined variable that is sent to the model function.
% Useful if the model need some parameters defined outside the DPM
% function.
% OPTIONS is the options structure containing
% OPTIONS.Waitbar = 'off'; (on/off to show or hide waitbars)
% OPTIONS.Verbose = 'on' (on/off command window status
% notification)
% OPTIONS.Warnings = 'off'; (on/off to show or hide warnings)
% OPTIONS.SaveMap = 'on'; (on/off to save cost-to-go map)
% OPTIONS.MyInf = 1e4; (a big number for infeaible states
% where out.I=1)
% OPTIONS.Minimize = 1; (one/zero if minimizing or maximizing)
% OPTIONS.InputType = 'cd' (string with the same number of
% characters as number of inputs.
% contains the character 'c' if input is
% continuous or 'd' if discrete.
% Default is all continuous.)
% OPTIONS.BoundaryMethod = 'none', 'Line' or 'LevelSet'
% if BoundaryMethod = 'Line'
% OPTIONS.FixedGrid = 0; (zero/one use grid as defined in GRD or
% adjust the according to boundary line)
% OPTIONS.Iter = 10; (maximum number of iterations when
% inverting model)
% OPTIONS.Tol = 1e-8; (minimum tolerance when inverting
% model)
% endif
% OPTIONS.gN{1} Cost matrix at the final time
% (must be of size(OPTIONS.gN{1}) =
% [GRD.Nx{1} GRD.Nx{2} ... GRD.Nx{.}]).
%
%
% OUT = DPM(DYN,FUN,PAR,GRD,PRB,OPTIONS) only calculates the forward
% simulation using DYN calculated earlier.
%
% OUT = DPM(N0,DYN,FUN,PAR,GRD,PRB,OPTIONS) only calculates the forward
% simulation using DYN calculated earlier but from index N0
% (in the range 1->prb.N).
%
% Up to 5e6 grid points (prod([GRD.Nx{1} GRD.Nx{2} ... GRD.Nx{.}
% GRD.Nu{1} GRD.Nu{2} ... GRD.Nu{.}])) works well.
%
%
% EXAMPLES_______________________________________________________________
% DPM can be used to get standard options
% options = dpm();
%
% DPM can be used to generate a test model
% dpm('model_test',3,2);
%
% FULL DYNAMIC PROGRAMMING EXAMPLES______________________________________
% To calculate the optimal control for a test model:
% dpm('model_test',2,2);
% grd.Nx{1} = 11; grd.Xn{1}.lo = -50; grd.Xn{1}.hi = 100;
% grd.Nx{2} = 11; grd.Xn{2}.lo = -50; grd.Xn{2}.hi = 100;
% grd.Nu{1} = 11; grd.Un{1}.lo = -5; grd.Un{1}.hi = 5;
% grd.Nu{2} = 11; grd.Un{2}.lo = -5; grd.Un{2}.hi = 5;
%
% grd.X0{1} = 0;
% grd.X0{2} = 0;
% grd.XN{1}.lo = 0; grd.XN{1}.hi = 20;
% grd.XN{2}.lo = 0; grd.XN{2}.hi = 20;
%
% prb.Ts = 1/5;
% prb.N = 200*1/prb.Ts + 1;
% prb.N0 = 1;
% prb.W{1} = rand(1,prb.N);
% options = dpm();
% [out dyn] = dpm('model_test',[],grd,prb,options);
%
%
% HINTS FOR DEBUGGING____________________________________________________
% The model function is called twice before the actual DP algorithm is
% used in order to determine the number of states, inputs, and outputs.
% When adding breakpoints to the model function, please be aware of this.
%
%
% REFERENCES_____________________________________________________________
% When using DPM please cite:
% Sundstrom, O. and Guzzella, L., "A Generic Dynamic Programming Matlab
% Function", In Proceedings of the 18th IEEE International Conference on
% Control Applications, pages 1625-1630, Saint Petersburg, Russia, 2009
%
% LICENSE________________________________________________________________
% This Source Code Form is subject to the terms of the Mozilla Public
% License, v. 2.0. If a copy of the MPL was not distributed with this
% file, You can obtain one at http://mozilla.org/MPL/2.0/.
%
% COPYRIGHT______________________________________________________________
% Copyright 2008- Institute for Dynamic Systems and Control, Department
% of Mechanical and Process Engineering, ETH Zurich
% Author: Olle L. Sundstrom
%
% CHANGELOG______________________________________________________________
% v.1.0.6 (2010) Useable for MATLAB 2007 -- CD
% v.1.0.6 (15-Dec-2010): Added OPTIONS.VERBOSE 'on'|{'off'}. Prints
% status of DPM in the command window. Output equivalent to Waitbar but
% with significantly less computational effort---SE
% v.1.0.6 (July 2011) removed use of roundn
% v.1.1.0 (15-Dec-2011) Added Level-Set-Method as an option and new
% forward simulation scheme as an option -- PE
% v.1.1.1 (11-Oc-2012) fixed error handling in line 2394 --PE
% v.1.1.2 (19-Juni-2013) added licence agreement header -- PE
try
varargout = {};
if nargin == 3
if ~exist([varargin{1} '.m'],'file')
str{1} = '';
str{end+1} = ['function [X, C, I, signals] = ' varargin{1} '(inp,par)'];
str{end+1} = '\n%% inp.X{i} states';
str{end+1} = '%% inp.U{i} inputs';
str{end+1} = '%% inp.W{i} disturbances (as defined in dis-struct)';
str{end+1} = '%% inp.Ts time step';
str{end+1} = '%% par struct including user defined parameters';
% str{end+1} = '%% lim.X{i} = ["lower" ; "upper"] (limits of each state)';
str{end+1} = '\n%% state update (out.X{i} must be set within model function)';
% str{end+1} = 'func = inp.Ts.*(par.a.*(inp.X{1}-inp.X{1}.^2/par.b)-inp.U{1});';
for i=1:varargin{2}
x = round(rand*(varargin{2}-1))+1;
u = round(rand*(varargin{3}-1))+1;
str{end+1} = ['X{' num2str(i) '} = ' num2str(rand) '.*(inp.X{' num2str(x) '} + inp.U{' num2str(u) '} + inp.W{1})./inp.Ts + inp.X{' num2str(i) '};'];
end
str{end+1} = '\n%% cost (out.C{1} must be set within model function)';
str{end+1} = 'C{1} = -inp.Ts.*inp.U{1};';
str{end+1} = '\n%% Infeasibility (out.I [zero=feasible/one=infeasible] must be set within model function)';
str{end+1} = '\n%% for example if the state is outside the grid or infeasible combinations of inputs and states occur.';
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