Kexin Wang

Quasi-weighted least squares estimator for data reconciliation

Data reconciliation is important in chemical industries. Because of random and possibly gross errors in measurements, data reconciliation is needed to minimize the measurement errors. The most common estimator for data reconciliation is the weighted least squares, which is not robust. A robust estimator, quasi-weighted least squares, is proposed for data reconciliation. The properties of the estimator are analyzed, and the influence function is used to show that the estimator is robust. Two estimators, weighted least squares and quasi-weighted least squares, are used in atmospheric tower, ethylene separation and air separation process systems. Comparisons with other approaches are made on the steam metering process. The effectiveness of the robust estimator is demonstrated.

Time-Optimal Maneuver Planning in Automatic Parallel Parking Using a Simultaneous Dynamic Optimization Approach

Autonomous parking has been a widely developed branch of intelligent transportation systems. In autonomous parking, maneuver planning is a crucial procedure that determines how intelligent the entire parking system is. This paper concerns planning time-optimal parallel parking maneuvers in a straightforward, accurate, and purely objective way. A unified dynamic optimization framework is established, which includes the vehicle kinematics, physical restrictions, collision-avoidance constraints, and an optimization objective. Interior-point method (IPM)-based simultaneous dynamic optimization methodology is adopted to solve the formulated dynamic optimization problem numerically. Given that near-feasible solutions have been widely acknowledged to ease optimizing nonlinear programs (NLPs), a critical region-based initialization strategy is proposed to facilitate the offline NLP-solving process, a lookup table-based strategy is proposed to guarantee the on-site planning performance, and a receding-horizon optimization framework is proposed for online maneuver planning. A series of parallel parking cases is tested, and simulation results demonstrate that our proposal is efficient even when the slot length is merely 10.19% larger than the car length. As a unified maneuver planner, our adopted IPM-based simultaneous dynamic optimization method can deal with any user-specified demand provided that it can be explicitly described.

Time-optimal trajectory planning for tractor-trailer vehicles via simultaneous dynamic optimization

Trajectory planning is a critical aspect of autonomous tractor-trailer vehicle design. Trajectory planning algorithms usually compute paths first, trajectories are obtained thereafter. This multi-step feature makes those planners inefficacious to handle time-dependent constraints. In this study, we consider the original trajectory planning mission directly, which is described as an optimal control problem containing the kinematics, mechanical/physical constraints, environmental requirements as well as an optimization criterion. In this formulation, only the fundamental driving principles with no special issues (e.g., backing-up maneuver and jackknife) are considered. For example, the prevailing “small-angle assumption” is not utilized to prevent jackknifing. Instead, we only require that different parts of a tractor-trailer vehicle should not collide, since the emergence of jackknife does not physically violate the kinematics. An interior-point method based simultaneous approach is adopted to solve the formulated optimal control problem. Simulation results verify our proposal is capable of handling scenarios with various user-specified requirements.

Robust extensions for reduced-space barrier NLP algorithms

Abstract Reduced-space barrier NLP algorithms are particularly useful for optimization of large structured systems with few degrees of freedom. Such optimization algorithms are often applied on process models developed within equation oriented process simulators. By partitioning the search direction into tangential and normal steps, these methods can exploit the structure of the equality constraints and adjust the remaining degrees of freedom in a lower dimensional space. Moreover, as shown in previous work, the barrier approach extended with a novel filter linear search algorithm has global and fast local convergence properties. However, convergence properties of the reduced-space barrier algorithm require regularity assumptions. In particular, the method may fail in the presence of linearly dependent active constraints. To deal with these questions, we modify the reduced-space barrier method in two ways. First, as the filter line search requires a feasibility restoration step, we develop and analyze an improved algorithm for this step, which is tailored to the reduced-space method. In addition, a dimension change procedure is proposed to address decomposition of problems with linearly dependent constraints. Finally, both approaches are implemented within a reduced-space version of IPOPT and numerical tests demonstrate the performance of the proposed modifications.

Barrier NLP methods with structured regularization for optimization of degenerate optimization problems

Abstract Barrier nonlinear programming (NLP) solvers exploit sparse Newton-based algorithms and are characterized by fast performance and global convergence properties. This makes them especially suitable for very large process optimization problems. On the other hand, they are frequently challenged by degenerate and indefinite problems, which lead to ill-conditioned Karush–Kuhn–Tucker (KKT) systems. Such problems arise when process optimization models contain linearly dependent constraints, or the reduced Hessian is not positive definite at the solution. This can lead to poor solver performance and may preclude finding successful NLP solutions. Moreover, such optimization models occur in blending problems and NLP subproblems generated by MINLP or global optimization strategies. To deal with these difficulties we present a structured regularization strategy for barrier methods that identifies and excludes dependent constraints in the KKT system while leaving independent constraints unchanged. As a result, more accurate Newton directions can be obtained and much faster convergence can be expected for the KKT system over the conventional regularization approach. Numerical experiments with examples derived from the CUTE and COPS test sets as well as two nonlinear blending problems demonstrate the effectiveness of the proposed method and significantly better performance of the NLP solver.

Reduced precision solution criteria for nonlinear model predictive control with the feasibility-perturbed sequential quadratic programming algorithm

We propose a novel kind of termination criteria, reduced precision solution (RPS) criteria, for solving optimal control problems (OCPs) in nonlinear model predictive control (NMPC), which should be solved quickly for new inputs to be applied in time. Computational delay, which may destroy the closed-loop stability, usually arises while non-convex and nonlinear OCPs are solved with differential equations as the constraints. Traditional termination criteria of optimization algorithms usually involve slow convergence in the solution procedure and waste computing resources. Considering the practical demand of solution precision, RPS criteria are developed to obtain good approximate solutions with less computational cost. These include some indices to judge the degree of convergence during the optimization procedure and can stop iterating in a timely way when there is no apparent improvement of the solution. To guarantee the feasibility of iterate for the solution procedure to be terminated early, the feasibility-perturbed sequential quadratic programming (FP-SQP) algorithm is used. Simulations on the reference tracking performance of a continuously stirred tank reactor (CSTR) show that the RPS criteria efficiently reduce computation time and the adverse effect of computational delay on closed-loop stability.

Dynamic optimization of multivariable endothermic reaction in cascade CSTR

The dynamic optimization problem of a multivariable endothermic reaction in cascade continuous stirred tank reactors is solved with simultaneous method in this paper. Radau collocation is applied in discretization because of its stiff decay and high precision. A two-layer optimization is presented to get a fast convergence rate when dealing with the nonlinear case. In the industry process, the load variation may be very large and may cause output variables big overshoot. In order to reduce the overshoot, a segmentation load variation method is introduced. The good results of this nonlinear ordinary differential equations system show the validity of these methods.

Dual adaptation strategy for model-based operation

Abstract Model-based operations are frequently challenged by unsatisfactory model accuracy, which hampers finding the true plant optimum. Integrated parameter estimation and optimization methods were proposed to handle the problem. However, they did not focus on improving model accuracy or confining optimization to a valid operating range. Dual adaptation strategy is thus presented in this paper to integrate local parameter model and real-time optimization through trust-region framework. On one hand, application range of the local model is decided adaptively so as to avoid invalid operations. On the other hand, the local model is updated adaptively for purpose of reducing plant-model mismatch in moderate cost. The above two aspects contribute to dual adaptation concept. It is guaranteed that the optimal operations derived from this dual adaptation strategy converge to the plant optimum. Case study of significant load change for HTR-PM demonstrates effectiveness of the proposed method.

Robust nonlinear model predictive control algorithm based on reduced precision solution criteria

This paper discusses the robustness of nonlinear model predictive control (NMPC) based on sub-optimal solution obtained under reduced precision solution (RPS) criteria. NMPC needs to solve the optimal control problem (OCP) quickly and the input is injected to the controlled plant in time. Traditional convergence criteria in optimization algorithms usually cost excessive long computation time with little improvement of solution, which results in degradation of control performance eventually. RPS criteria are new convergence criteria for deciding whether the current iterate is good enough and whether the optimization procedure should be terminated. It can terminate the optimization process timely. This work pays special attention to robustness of the closed-loop system controlled by NMPC with RPS criteria when model plant mismatch exists. Simulations demonstrate that the proposed algorithm owns good robustness and stability.

Structured regularization in barrier NLP for optimization models with dependent constraints

Abstract Global convergence and fast performance of barrier nonlinear programming (NLP) solvers are frequently challenged by linearly dependent constraints. Such constraints arise in many process optimization models, and they often preclude finding successful NLP solutions. To deal with this problem we present a structured regularization strategy for barrier methods that identifies and excludes dependent constraints in the KKT system while leaving independent constraints unchanged. As a result, more accurate Newton directions can be obtained and much faster convergence can be expected for the KKT system over the conventional regularization approach. Numerical experiments with examples derived from the CUTE and COPS test sets as well as two refinery blending problems demonstrate the effectiveness of the proposed method and significantly better performance of the NLP solver.