MPT 2.0.2 Changelog


Permanent saving of options in mpt_init

mpt_init can now permanently save list of available solvers, such that consequent runs of mpt_init are performed much faster. to utilize the new feature, call: 
  >> mpt_init('save')
if you want to set some default options, e.g. if you want to use CDD as default LP solver and change value of absolute tolerance to 1e-8, call: 
  >> mpt_init('lpsolver', 'cdd', 'abs_tol', 1e-8, 'save');
Note! if you install some new solvers after you save the settings, this change will not be reflected by MPT. in order to tell MPT to find your new solver, call:
  >> mpt_init('rehash')

Assign objects in caller's workspace

This cryptic name roughly means the following: when you use certain functions, the result is automatically updated in the workspace, without the need to request the output from the function explicitly. To illustrate this, take for instance the mpt_simplify function, which tries to simplify regions of an explicit controller: 
  >> Double_Integrator;
  >> ctrl = mpt_control(sysStruct, probStruct);
Now we have the variable ctrl in our main workspace. In order to simplify the controller, one can call: 
  >> ctrl_simple = mpt_simplify(ctrl)
or, with the new syntax, just call: 
  >> mpt_simplify(ctrl)
The new syntax internally does the following: 
  >> ctrl_dummy = mpt_simplify(ctrl)
  >> ctrl = ctrl_dummy
  >> clear ctrl_dummy
i.e. it updates the ctrl variable in your workspace such that it nows contains the simplified controller. The old syntax of course works as well.
Following functions can be used in the new way: 
  >> mpt_lyapunov(ctrl, function_type)
  >> mpt_invariantSet(ctrl)
  >> mpt_simplify(ctrl)
  >> mpt_searchTree(ctrl)

Major speedup of invariant sets computation and Lyapunov functions calculations

Thanks to Johan Löfberg, mpt_invariantSet and mpt_lyapunov now exploit mpt_transmap which allows to prune infeasible transitions very quickly. This results in speedup typically by factor of 5-10.

New mpLP solvers

Miroslav Baric prepared 2 new mpLP solvers (mpt_mplp_ver6.m and mpt_mplp_ver7.m), which are significantly more numerically robust than previous versions.

New function to compute orthogonal cuts through polytope(s)

Frank J. Christophersen coded polytope/slice.m which calculates orthogonal cut through a polytope or a polytope array: 
  >> Pcut = slice(P, coords, values)
where coords is a vector of coordinates through which to cut and values is a vector of values at which to cut.

merge.m now allows to use optimal merging

Tobias Geyer contributed an update to polytope/merge.m which allows to use the optimal merging: 
  >> Options.greedy = 0; % use optimal merging instead of greedy method
  >> Pm = merge(P, Options);

Improved analytical computation of convex hulls for dimensions above 2

Mario Vasak contributed an update of the hull.m function, which allows to solve convex hull problems more efficiently and more robustly.

New function to simulate MLD systems - mpt_mldsim

Allows to simulate a given MLD system for one time step by solving a feasibility mixed-integer program: 
  >> [xn,y,d,z] = mpt_mldsim(S, x0, u)
where S is a structure containing matrices of the MLD system, x0 is the initial state and u is the control input.
This type of simulation can also be used from mpt_simSys if Options.usemldsim=1: 
  >> Options.usemldsim = 1;
  >> [X,U,Y] = mpt_simSys(sysStruct, x0, U, Options);

Create sysStruct structure based on MLD matrices

mpt_sys now allows to use the following scenario: 
  >> sysStruct = mpt_sys(S, 'nopwa')
i.e. it creates a sysStruct structure based on MLD matrices without transforming the hybrid system into an equivalent PWA representation.

Penalties on d and z variables can now be specified

When solving an on-line MPC problem for MLD systems, penalties on boolean d and on auxiliary continuous z variables can now be specified: 
  >> probStruct.Qd = Qd
  >> probStruct.Qz = Qz

New function to plot Lyapunov functions

mpt_plotLyapunov will plot a Lyapunov function stored in a given controller object: 
  >> ctrl_lyap_pwq = mpt_lyapunov(ctrl, 'pwq')
  >> ctrl_lyap_pwa = mpt_lyapunov(ctrl, 'pwa')
  >> mpt_plotLyapunov(ctrl_lyap_pwq)
  >> mpt_plotLyapunov(ctrl_lyap_pwa)
Note: works for PWQ and PWA Lyapunov functions, does not work for Piecewise-Polynomial and SOS Lyapunov functions.

Verification of hybrid systems based on feasibility MILP

The question of verifying if a given hybrid system can enter a given target set in finite time can now be formulated and solved as a feasibility Mixed-Interger LP: 
  >> Options.usereachsets = 0; % use MILP instead of reachable sets
  >> answer = mpt_verify(sysStruct, X0, Xf, N, U0, Options);

Allow terminal state and terminal set constraints for on-line MPC for MLD systems

On-line MPC controllers for MLD systems can now be instructed to obey terminal point and terminal set constraints: 
  >> probStruct.xN = xN;     % to use terminal point constraint
  >> probStruct.Tset = Tset; % to use terminal set constraint

Allow time-varying penalties for on-line MPC problems for MLD systems

On-line MPC controllers for MLD systems can now use time-varying penalties on states, inputs, outputs, d and z variables. To define a penalty as being time-varying, simply assign it to a cell array: 
  >> probStruct.Q = {Q1, Q2, ..., Qn};
  >> probStruct.R = {R1, R2, ..., Rn};
  >> probStruct.Qy = {Qy1, Qy2, ..., Qyn};
  >> probStruct.Qd = {Qd1, Qd2, ..., Qdn};
  >> probStruct.Qz = {Qz1, Qz2, ..., Qzn};

Handle time-varying output penalties in explicit MPC for LTI systems

For explicit solutions for LTI systems, penalties on outputs can now be time-varying by specifying probStruct.Qy as a cell array: 
  >> probStruct.Qy = {Qy1, Qy2, ..., Qyn};

Other notable improvements and bugfixes

Acknowledgment

We are grateful to the following people for interesting comments and feedback: Andrea G. Beccuti, Arne Linder, Arno van der Heijden, Hao Xia, Jian Wan, J.S. Wang, Marcin Cychowski, Peter Ortner, Raphael Cagienard, Tina Paschedag.