(441h) Robust Explicit Optimization and Control within the Paroc Framework

The presence of uncertainty in process systems is one of the key reasons for deviation from set operation policies, resulting in suboptimal or even infeasible operation. As these uncertainties realize themselves on different time scales such as on a control, scheduling or design level, an integrated, comprehensive approach to consider uncertainty is required. For that reason, the PARametric Optimization and Control Framework (PAROC) which decomposes this challenging problem into a series of steps and computes explicit solutions was developed [1-4]. Robust optimization aims to immunize against uncertainty by guaranteeing constraint satisfaction [5]. In robust rolling horizon optimization of discrete-time systems, such as MPC, the derivation of robust optimization policies is mainly characterized by the challenge associated with multiplicative uncertainty [6-9]. The concept of explicit/multiparametric robust rolling horizon optimization aims to provide the explicit form of the closed-loop robust rolling horizon policy known “in the present” that can guarantee feasibility “in the future” [10-12].

In this work, we consider the development of closed-loop explicit robust rolling horizon solutions that correspond to MPC and scheduling problems and their applicability within the PAROC framework, i.e. their utilization in design, control, scheduling problems and their interactions. We consider box-constrained model uncertainty on linear state-space problems upon which we (i) formulate the robust counterpart in a single-step problem formulation, (ii) apply linear transformations to acquire the feasible space as a function of the initial state value realizations and the degrees of freedom and (iii) apply multi-parametric (mixed-integer) programming to acquire the explicit solution of the problem. With this approach, we show (i) how the need for a dynamic programming approach can be alleviated while (ii) guaranteeing the robust nature of the final solution and (iii) we extend the approach to the hybrid case where both integer and continuous variables can be considered via [13]. We present the developments through examples of control, scheduling and design optimization problems.

References

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