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Hybrid Toolbox for Matlab

The Hybrid Toolbox is a MATLAB/Simulink toolbox for modeling, simulating, and verifying hybrid dynamical systems, for designing and simulating model predictive controllers for hybrid systems subject to constraints, and for generating linear and hybrid MPC control laws in piecewise affine form that can be directly embedded as C-code in real-time applications.

The main features of the toolbox are:

Hybrid model design and simulation

• 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.

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 control design

• Piecewise affine controllers can be designed via offline optimization (multiparametric programming) for linear systems w/ constraints and for hybrid systems.
• MPC controllers designed for linear constrained systems with the new Model Predictive Control Toolbox for MATLAB can be also converted into piecewise affine form via multiparametric quadratic programming.

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
  • QP solver of the MPC Toolbox (The Mathworks)
  • LP/QP/MILP/MIQP solvers of Cplex (Ilog, Inc.)
  • (CPLEXMEX, CPLEXINT and IBM ILOG Cplex Mex)
  • 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.)
  • MIQP.M (free, now included in the toolbox)

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.

Official Web Page and Download

To download the Hybrid Toolbox for Matlab please go to the Official Web Site

Author

Prof. Alberto Bemporad