prof. Ing. Vladimír Havlena, CSc.

industry as the safety constraints, performance constraints and economic objectives can be easily incorporated in the controller design. Extensions to non linear MPC are typically limited by computational complexity of underlying algorithms. Utilization of specific problem structure and Iteration Spread in Time approach may provide applicable algorithms, but also further theoretic development is needed e.g. to guarantee the feasibility of solution after each iteration. Feasibility constrained methods are also relevant in other industrial applications - Real Time Optimization and receding horizon state estimation. Topic 1: Develop, implement and analyze feasibility constrained optimization algorithms for MPC using continuous-time model and multishooting problem formulation.Topic 2: Develop, implement and analyze feasibility constrained optimization algorithms for RTO with possibly decentralized implementation.Topic 3: Develop, implement and analyze optimization algorithms for moving horizon state estimation.Topic 4: Develop and implement tool for grey box identification with focus on MPC applications (optimization of multistep prediction error). http://dce.fel.cvut.cz/katedra/prof-ing-vladimir-havlena-csc

This doctoral research Framework proposal builds on recent development and breakthroughs in availability of large data sets (process historical data), hardware (parallel processing using banks of GPU) and AI/ML algorithms (expanding from complete state information applications to incomplete state information and incorporation of uncertainty). Under this Framework proposal, several more specific research topics can be specified: 1. By integration of control science and data science we can reopen hard control problems (curse of dimensionality in dual control) and look for new solutions using tools from AI domain (exploration/exploitation trade-off in AI). 2. By combining model-based and model-less approaches we can improve the quality and applicability of control, expanding out of the linear dynamics assumption. Model-based dynamic optimization provides optimal control solution with guaranteed stability and robustness, however, fine tuning of the model or switching from a local linear model to global non-linear one in case of performance issues can become a never ending story, demanding on domain knowledge. On the other hand, switching from model-based control law to properly initialized model-less Q-learning and direct optimization of control policy using real-time process data can be more straightforward solution, easy to turn into generic algorithms. 3. There are many results linking the robust control theory and game theory, however, in many cases the conservative worst case (min/max) scenarios result in overly cautious control with limited bandwidth, not acceptable for practical applications. Methods of AI based on sampling “typical“ uncertainty can lead to more efficient robust control design methods. 4. Gaussian process regression. Majority of system identification methods using state-space approach is based on parametric models. Gaussian process regression provides an alternative, covering much broader class of systems. At the same time, the kernel function provide powerful tool for incorporation of prior information. Gaussian process regression is also an efficient tool for function approximation e.g. in Q-learning as an alternative or complement to neural networks.  Rathousky, Jan; Havlena, Vladimir: MPC-based approximate dual controller by information matrix maximization. International Journal of Adaptive Control and Signal Processing, Volume 27, Issue 11, Pages 974-999, 2013.