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dynamics.m

+%% Tutorial example on symbolic control
+%% Author: Antoine GIRARD, Universit Paris-Saclay, CNRS, CentraleSuplec, Laboratoire des signaux et systmes, 91190, Gif-sur-Yvette, France.
+%% Date: 2024
+
+
+%% Definition of the dynamics of the system and of abstraction parameters
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% System Definition
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+% Sampling time 
+T=1;
+
+% System dynamics
+f=@(x,u,w) [x(1)+T*u(1)*cos(x(3))+T*w(1);...
+            x(2)+T*u(1)*sin(x(3))+T*w(2);...
+            x(3)+T*u(2)+T*w(3)];
+
+% Bounds on Jacobian matrices for over-appoximation of reachable sets
+Jf_x=@(u) [1 0 T*abs(u(1));...
+           0 1 T*abs(u(1));...
+           0 0 1];
+
+Jf_w=@(u) [T 0 0;...
+           0 T 0;...
+           0 0 T];
+       
+% Constraints
+bound_x=[0 10;0 10;-pi pi];                   % State Constraints
+bound_u=[0.25 1;-1 1];                        % Control Constraints
+bound_w=[-0.05 0.05;-0.05 0.05;-0.05 0.05];   % Disturbance Constraints
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Abstraction parameters
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%Symbolic parameters
+n_x=[100;100;30];                        % Number of state partition cells
+n_u=[3;5];                               % Number of control partition cells