Note: This content is accessible to all versions of every browser. However, this browser does not seem to support current Web standards, preventing the display of our site's design details.

Control of Constrained Hybrid Systems

Main Research Topics

Main Research Topics


We have produced a number of results on modeling of discrete-time hybrid dynamical systems. Depending on the intended application, a different approach might provide better tools:

Control Synthesis

Most hybrid system models, including those described on our website on modeling of hybrid systems, require or enable specialized approaches to controller synthesis. We have put effort into this along different lines:

  • Model predictive control (MPC): we have produced a significant number of fundamental results on MPC of both linear and hybrid systems
  • Online and explicit MPC: optimization based control methods such as MPC might be applicable to dynamical systems with fast sampling times by trading off the distinct advantages of online and offline (explicit) computations
  • Robust control: in the presence of disturbances and measurement noise, special care must be taken to maintain stability of the dynamical system


For many hybrid system models we provide results and tools for analysis of different system properties such as stability, reachability, and verification of specifications:

Computational Issues

To facilitate the application of the developed theory to real systems, we investigate how algorithms and tests can efficiently be implemented on modern hardware:

  • Complexity reduction: for most control tasks it is beneficial to have as simple a description of the system as possible
  • Computational geometry: because many hybrid system descriptions rely on efficient polytope manipulations we develop on provide some dedicated tools
  • Lagrangian decomposition: for interconnections of large numbers of hybrid systems, dual decomposition approaches can be applied to solve the MPC optimization problems


The problem of estimating the system state from measurable outputs of a hybrid system is not as well-understood as the analogous problem for linear systems. We present some techniques that rely on the estimation problem being dual to the control problem and therefore allows for similar techniques:

  • Moving horizon estimation: the receding horizon principle of MPC can also be applied to estimate the state of PWA and MLD systems
  • Fault detection: similar to (but distinct from) the estimation problem, fault detection aims to identify significant changes in the plants behavior from input-output-data


Hybrid systems are quite ubiquitous in physical applications. In most cases the challenge is in obtaining a good model the plant as well as implementing modern control algorithms on available hardware. We present here a number of applications where the developed theory leads to superior process operation:

  • Automotive: common control tasks in cars such as traction control, cruise control, and the control of an electronic throttle can benefit from applying hybrid system theory
  • Active damping: many damping applications contain switching components which can be modeled using one of the hybrid system frameworks presented above
  • Hydropower: for optimal hydropower plant operation it is beneficial to take into account both knowledge of future and about discrete dynamics of the system which makes MPC a good tool to use in this case