Lihui Cen

Probabilistic constrained stochastic model predictive control for Markovian jump linear systems with additive disturbance

Abstract This paper is concerned with stochastic model predictive control for Markovian jump linear systems with additive disturbance, where the systems are subject to soft constraints on the system state and the disturbance sequence is finitely supported with joint cumulative distribution function given. By resorting to the maximal disturbance invariant set of the system, a model predictive control law is given based on a dynamic controller which is with guaranteed recursive feasibility and ensures the probabilistic constraints on the states. By optimizing the volume of the disturbance invariant set, the dynamic controller is given. The closed loop system under this control law is proven to be stable in the mean square sense. Finally, a numerical example is given to illustrate the developed results.

Boundary feedback control of open canals with a Riemann invariants approach

This paper proposes a boundary feedback control design for open canal networks using the linearization of boundary conditions. For open canal networks with any types of cross-sections, which can be modelled by the Saint-Venant equations, the characteristic form in terms of Riemann invariants has been established. Under this established characteristic form, the stabilizing boundary control law has been developed by linearizing the boundary conditions for both a single reach and the open-channel network composed by multi-reaches in a cascade. The design of the boundary feedback control laws for both a single canal and the cascaded networks is illustrated in a unified framework, which extends the results in the literature.

Energy-saving optimization of urban drainage system based on pump performance

To reduce wastewater overflow and high power cost caused by unreasonably operating pump device in urban drainage system, a pump performance-based energy optimization strategy is proposed. A mathematical model is built based on the typical topological structure of urban drainage systems, and the calculation equations for sewerage inflow, outflow and storage condition of relevant pumping stations are established. Previous energy saving optimization algorithm regard pump efficiency as linear which limits the optimization result. To guarantee the energy saving effect, a nonlinear mathematical model of pump performance is constructed. According to the nonlinear relationships among pump flow, head and efficiency, total energy consumption in the next two time-domain is predicted. Energy consumption of the system can be reduced by optimizing the outflow of relevant pump stations dynamically. Comparing with traditional control methods of urban drainage system, the simulation results demonstrate that the proposed optimization algorithm can reduce system energy consumption as well as avoid wastewater overflow efficiently.

Boundary Feedback Stabilization and Control of Star-shaped Open Canals

Abstract This paper considers the boundary control of a star-shaped open-channel network modeled by the Saint-Venant equations. We present the boundary feedback stabilization of the Saint-Venant equations by means of a Riemann invariants method. The estimation of the parameters satisfying the stability condition is deduced. The boundary feedback control is developed to guarantee that the solution of the control system decays exponentially, only by taking the water levels at the gate boundaries as the feedback.

On Modeling and Constrained Model Predictive Control of Open Irrigation Canals

This paper proposes a model predictive control of open irrigation canals with constraints. The Saint-Venant equations are widely used in hydraulics to model an open canal. As a set of hyperbolic partial differential equations, they are not solved explicitly and difficult to design optimal control algorithms. In this work, a prediction model of an open canal is developed by discretizing the Saint-Venant equations in both space and time. Based on the prediction model, a constrained model predictive control was firstly investigated for the case of one single-pool canal and then generalized to the case of a cascaded canal with multipools. The hydraulic software SICC was used to simulate the canal and test the algorithms with application to a real-world irrigation canal of Yehe irrigation area located in Hebei province.

Formulation of MPC for Multiplicative Stochastic Uncertainty by Multi-step Probabilistic Sets

Abstract This paper designs multi-step probabilistic sets for linear, discrete-time, stochastic systems with unbounded multiplicative noise and probabilistic constraints. Multi-step probabilistic sets strengthen IWPp by bringing more degrees of freedom to optimize the applicable region of finite-step probabilistic constraints, and extending the prediction horizon of IWPp to infinity for infinite-horizon probabilistic constraints. Conditions for multi-step probabilistic sets are then incorporated into a stochastic model predictive control algorithm to satisfy probabilistic constraints. Closed-loop mean-square stability is guaranteed by the algorithm. A numerical example shows the performance of the proposed algorithm.