Hybrid Toolbox - Hybrid Systems, Control, Optimization

Hybrid systems modelling, simulation, and analysis

Mixed logical dynamical (MLD) systems are handled as MATLAB objects, obtained from HYSDEL models.

MLD objects can be automatically converted into piecewise affine (PWA) objects.

MLD and PWA objects can be simulated in MATLAB or in Simulink.

Safety properties can be verified through reachability analysis.

Model predictive control design

Model predictive controllers based on on-line optimization (MILP / MIQP) can be designed for hybrid systems.

Quadratic and infinity norms are supported.

Explicit MPC control design

Explicit MPC controllers in piecewise affine form can be designed via offline optimization (multiparametric programming) for linear systems w/ constraints and for hybrid systems.

C-code generation

Explicit controllers can be easily exported as C-code for direct implementation and rapid prototyping, by either simply running Real-Time Workshop or by embedding the generated C code in the application.

Simulink library

Blocks are provided for: controllers based on on-line optimization, explicit piecewise linear controllers, MLD and PWA models.

Solver support

The Hybrid Toolbox supports several solvers for linear, quadratic, and mixed-integer optimization.

List of supported solvers:

GNU Linear Programming Kit (GLPKMEX) for LP/MILP
GUROBI for LP/QP/MILP/MIQP (Gurobi Optimization, Inc.)
LP/QP/MILP/MIQP solvers of Cplex (Ilog, Inc.)
(CPLEXMEX, CPLEXINT, and IBM Cplex)
LP/QP/MILP/MIQP solvers of Xpress-MP (Dash Optimization) (MEXPRESS)

LP/QP solvers of the NAG Foundation Toolbox

LP/QP solvers of the Optimization Toolbox (The Mathworks, Inc.)
QPKWIK solver of the Model Predictive Control Toolbox (The Mathworks, Inc.)
MIQP.M (free, now included in the toolbox)

Code/Manual Download (Version 1.4.8 - February 3, 2024)

Note: The code can be downloaded only for non-commercial use at universities, governmental entities, or academic non-profit institutions. An academic non-profit institution is defined by its mission: research in the public domain and education. A non-profit organization that performs research as a service under contract to a commercial entity does not belong to the category of non-commercial users. Commercial users interested in obtaining the code should contact the author Alberto Bemporad.

Citations to the toolbox manual are appreciated:

@MISC{HybTBX,
   author = {A. Bemporad},
   title = {{Hybrid Toolbox - User's Guide}},
   note={\url{http://cse.lab.imtlucca.it/~bemporad/hybrid/toolbox}},
   year = {2004},
}

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Author: Alberto Bemporad