SUMMARYThis paper extends tube-based model predictive control of linear systems to achieve robust control of nonlinear systems subject to additive disturbances. A central or reference trajectory is determined by solving a nominal optimal control problem. The local linear controller, employed in tube-based robust control of linear systems, is replaced by an ancillary model predictive controller that forces the trajectories of the disturbed system to lie in a tube whose center is the reference trajectory thereby enabling robust control of uncertain nonlinear systems to be achieved.

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SUMMARYPredictive control of nonlinear systems is addressed by embedding the dynamics into an LPV system and by computing robust invariant sets. This mitigates the on-line computational burden by transferring most of the computations off-line. Benefits and conservatism of this approach are discussed in relation with the control of a critical mechanical system.

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Existing stabilizing conditions that use a terminal cost and constraint that, if satisfied, ensure stability and recursive feasibility for deterministic, robust, and stochastic model predictive control are briefly reviewed and analyzed. It is pointed out that these conditions do not cover all situations. Proposals are made to cover a wider range of desired applications.KEYWORDS descent property, model predictive control, recursive feasibility, stabilizing conditions 894

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Abstract-Achieving the ambitious climate change mitigation objectives set by governments worldwide is bound to lead to unprecedented amounts of network investment to accommodate low-carbon sources of energy. Beyond investing in conventional transmission lines, new technologies such as energy storage can improve operational flexibility and assist with the costeffective integration of renewables. Given the long lifetime of these network assets and their substantial capital cost, it is imperative to decide on their deployment on a long-term costbenefit basis. However, such an analysis can result in large-scale Mixed Integer Linear Programming (MILP) problems which contain many thousands of continuous and binary variables. Complexity is severely exacerbated by the need to accommodate multiple candidate assets and consider a wide range of exogenous system development scenarios that may occur. In this manuscript we propose a novel, efficient and highly-generalizable framework for solving large-scale planning problems under uncertainty by using a temporal decomposition scheme based on the principles of Nested Benders. The challenges that arise due to the presence of non-sequential investment state equations and sub-problem non-convexity are highlighted and tackled. The substantial computational gains of the proposed method are demonstrated via a case study on the IEEE 118 bus test system that involve planning of multiple transmission and storage assets under longterm uncertainty. The proposed method is shown to substantially outperform the current state-of-the-art. All the parameters involved in the optimization model can be represented by the vector ρ containing B n,g Bus-to-generation incidence matrix. I n,ℓ Bus-to-line incidence matrix. S n,s Bus-to-storage incidence matrix.

Combining predictive control, LPV (Linear Parameter Varying) embedding and gainscheduling ideas, new computationally efficient algorithms for tracking control of constrained nonlinear systems are proposed. Simulation experiments demonstrate the good tracking properties of such algorithms.