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Concepts, algorithms and modeling platforms are described for the realization of nonlinear model predictive control (NMPC) using nonlinear programming (NLP). These allow the incorporation of predictive dynamic models that lead to high performance control, estimation and optimal operation. This talk reviews NLP formulations that guarantee properties for Lyapunov stability and extend to horizon lengths, terminal regions and costs. Moreover, fast algorithms for NMPC are briefly described and extended to deal with sensitivity-based solutions, as well as parallel decomposition strategies for large dynamic systems. Finally, Pyomo, a python-based modeling platform is tailored to deal with dynamic optimization strategies for state estimation, control and simulation, in order to incorporate all of these topics for on-line applications.

Forecasts play an increasingly important role in the next generation of autonomous and semi-autonomous systems. Applications include transportation, energy, manufacturing and healthcare systems.
Predictions of systems dynamics, human behavior and environment conditions can improve safety and performance of the resulting system. However, constraint satisfaction, performance guarantees and real-time computation are challenged by the growing complexity of the engineered system, the human/machine interaction and the uncertainty of the environment where the system operates.
Our research over the past years has focused on predictive control design for autonomous systems performing iterative tasks. In this talk I will first provide an overview of the theory and tools that we have developed for the systematic design of learning predictive controllers. Then, I will focus on recent results on the use of data to efficiently formulate stochastic MPC problems which autonomously improve performance in iterative tasks. Throughout the talk I will focus on autonomous cars to motivate our research and show the benefits of the proposed techniques.

The autonomous operation of highly complex devices, such as automotive vehicles, spacecraft, and precision manufacturing machines, usually requires an equally complex control software architecture, with several interacting control functions structured in layers and hierarchies. The integration of these control functions is a daunting task, hard, time consuming and expensive, and often the bottleneck to introducing new control algorithms into mass marketed products. In this talk we discuss how model predictive control (MPC) can simplify, if not solve entirely, the design of such complex control architectures. In particular, we discuss how MPC can be used in designing and enforcing assume-guarantee contracts between control functions that allow for their seamless integration with provable guarantees for the resulting architecture. Due to the generality of the enforceable contracts, these can be used to integrate control functions using different abstractions, update frequencies, and computational frameworks, such as in the architecture of autonomous ground or space vehicles, or to integrate control functions with other algorithmic frameworks, such as learning. The potential impact on several industrial domains is demonstrated with applications in automotive, aerospace and factory automation.

Motivated by practical applications, MPC formulations suitable for counteracting system drift, the effects of large measured disturbances/set-point changes, and overcoming limitations of under-actuation will be highlighted. 

For drift counteraction, where the objective is to maximize the time or yield until the system trajectory exits a prescribed set, defined by system safety constraints, operating limits and/or efficiency requirements, MPC, based on mixed integer or conventional linear programming, can lead to effective solutions for higher order systems than possible with dynamic programming and value iterations based methods. Such solutions can have a broad applicability including for fuel optimal Geostationary Orbit (GEO) station keeping, spacecraft Low Earth Orbit (LEO) maintenance, under-actuated spacecraft attitude control, hybrid electric propulsion energy management, glider flight management, and the development of driving policies for adaptive cruise control and autonomous driving.
Another intriguing capability of MPC to achieve non-smooth local stabilization of under-actuated systems will be highlighted and shown that it can be exploited for attitude control of under-actuated spacecraft with reaction wheel failures. Related results for systems that cannot be globally stabilized by continuous feedback will also be briefly mentioned.
Finally, opportunities to handle large load and set-point changes with reference governors will be discussed. These include combining reference governors with MPC schemes.

MPC has long been a source of challenges to optimization methodology, because of the need to tackle difficult, structured optimization problems in limited wall-clock time and in a way that meets the requirements of the controller (for example, stability). Recently, the interaction between optimization and MPC has taken on a new dimension, with new proposals being made for the use of machine learning (and thus optimization) in control strategies in which the models are learnt rather than specified. We review several of these developments from an optimization perspective, and speculate about how recent developments in nonconvex optimization and in MPC might impact each other in future.