Inverse scheduling with maximum lateness objective

We study a range of counterparts of the single-machine scheduling problem with the maximum lateness criterion that arise in the context of inverse optimization. While in the forward scheduling problem all parameters are given and the objective is to find the optimal job sequence for which the value of the maximum lateness is minimum, in inverse scheduling the exact values of processing times or due dates are unknown, and they should be determined so that a prespecified solution becomes optimal. We perform a fairly complete classification of the corresponding inverse models under different types of norms that measure the deviation of adjusted parameters from their given estimates.     

Optimal and suboptimal solutions to stochastically uncertain problems of quintile optimization

In this paper, problems of stochastic optimization under incomplete information on distribution of random perturbations with the quintile and probability criteria are considered. The minimax approach is used when optimal solutions are chosen. Conditions for equivalency of direct and inverse problems of stochastic optimization under incomplete statistical information are studied. The solution method for statistically uncertain problems of optimization with the quintile criterion basing on the use of generalized confidence sets for statistically uncertain random quantities is proposed. The use of confidence sets for finding suboptimal solutions to the problem of stochastic optimization under incomplete information is considered. Examples of the application of obtained relations are represented.     

From human to humanoid locomotion—an inverse optimal control approach

The purpose of this paper is to present inverse optimal control as a promising approach to transfer biological motions to robots. Inverse optimal control helps (a) to understand and identify the underlying optimality criteria of biological motions based on measurements, and (b) to establish optimal control models that can be used to control robot motion. The aim of inverse optimal control problems is to determine—for a given dynamic process and an observed solution—the optimization criterion that has produced the solution. Inverse optimal control problems are difficult from a mathematical point of view, since they require to solve a parameter identification problem inside an optimal control problem. We propose a pragmatic new bilevel approach to solve inverse optimal control problems which rests on two pillars: an efficient direct multiple shooting technique to handle optimal control problems, and a state-of-the art derivative free trust region optimization technique to guarantee a match between optimal control problem solution and measurements. In this paper, we apply inverse optimal control to establish a model of human overall locomotion path generation to given target positions and orientations, based on newly collected motion capture data. It is shown how the optimal control model can be implemented on the humanoid robot HRP-2 and thus enable it to autonomously generate natural locomotion paths.     

Mathematical programs with complementarity constraints in the context of inverse optimal control for locomotion

In this paper an inverse optimal control problem in the form of a mathematical program with complementarity constraints (MPCC) is considered and numerical experiences are discussed. The inverse optimal control problem arises in the context of human navigation where the body is modelled as a dynamical system and it is assumed that the motions are optimally controlled with respect to an unknown cost function. The goal of the inversion is now to find a cost function within a given parametrized family of candidate cost functions such that the corresponding optimal motion minimizes the deviation from given data. MPCCs are known to be a challenging class of optimization problems typically violating all standard constraint qualifications (CQs). We show that under certain assumptions the resulting MPCC fulfills CQs for MPCCs being the basis for theory on MPCC optimality conditions and consequently for numerical solution techniques. Finally, numerical results are presented for the discretized inverse optimal control problem of locomotion using different solution techniques based on relaxation and lifting.     

使用TAST码的BI-STCM-ID系统中的星座映射分析

研究了BI-STCM-ID系统中的星座映射问题.证明了在使用TAST空时编码方案的BI-STCM-ID系统中,基于最大化编码增益的高维星座映射设计优化问题等价于基于最大化欧式距调和均值的一维星座映射设计优化问题.     

使用LDC码的BI-STCM-ID系统中的星座映射分析

研究了BI-STCM-ID系统中的星座映射问题。证明了在使用LDC（Linear Dispersion Code）空时编码方案的BI-STCM-ID系统中,基于最大化编码增益的高维星座映射设计优化问题等价于基于最大化欧式距调和均值的一维星座映射设计优化问题。     

2D inverse problem in a distributed parameter system

In this paper, we present a numerical solution for an inverse heat problem to estimate 2D space-wise coefficient in a parabolic system describing heat transfer. The inverse problem is recast into an optimization problem solved with a conjugate gradient method. This approach use the non linear optimization formulation by minimizing a cost function taking into account both the measured outputs of the system and the outputs calculated by means of the model. The solution is performed by using the free finite element software FreeFem. Numerical example is carried out to check the validity of the proposed method.     

Robustness optimization in LQG multivariable systems with time-varying non-linear perturbations

This paper presents an algorithm to synthesize a controller in order to treat the problem of robustness optimization in LQG (linear-quadratic-gaussian) multi-variable systems subjected to time-varying non-linear perturbations. The controller not only minimizes the cost functional in LQG problems but also maximizes the excess robustness with respect to the Hardy H^∞-norm criterion by selecting two frequency-dependent weighting matrices Q(s) and R(s). Our approach is based on the Wiener-Hopf technique (frequency domain approach) and two weighting matrices in the cost functional are shaped by the inverse LQG method to achieve the robustness optimization. Furthermore, the plant of the system has no stable, proper, square, and minimum phase constraints. An example is given to illustrate our result.     

Adaptive fuzzy model based inverse controller design using BB-BC optimization algorithm

The use of inverse system model as a controller might be an efficient way in controlling non-linear systems. It is also a known fact that fuzzy logic modeling is a powerful tool in representing nonlinear systems. Therefore, inverse fuzzy model can be used as a controller for controlling nonlinear plants. In this context, firstly, a new fuzzy model based inverse controller design methodology is presented in this study. The design methodology introduced here is based on a recursive optimization procedure that searches for an optimal inverse model control signal at every sampling time. Since the task of optimization should be accomplished in between two sampling periods the use of a fast optimization algorithm becomes essential. For this reason, Big Bang-Big Crunch (BB-BC) optimization algorithm is used due to its low computational time and high global convergence properties. Even though, inverse model controllers may produce perfect control while operating in an open loop fashion, this open loop control would not be sufficient in the case of modeling mismatches or disturbances that might occur over the system. In order to overcome this problem, secondly, an on-line adaptation mechanism via BB-BC optimization algorithm is introduced in addition to BB-BC optimization based fuzzy model inverse controller. The adaptation mechanism is used to update the related parameters of the model while minimizing the absolute value of the instantaneous error between the system and model outputs. In this manner, the system output is somehow fed back, the overall control form can be considered as a closed-loop system. The new fuzzy model based inverse control scheme with the new online adaptation mechanism has been implemented and tested on the two real time processes; namely, heat transfer and pH processes and very satisfactory results has been reported.     

Parametric image alignment using enhanced correlation coefficient maximization

In this work we propose the use of a modified version of the correlation coefficient as a performance criterion for the image alignment problem. The proposed modification has the desirable characteristic of being invariant with respect to photometric distortions. Since the resulting similarity measure is a nonlinear function of the warp parameters, we develop two iterative schemes for its maximization, one based on the forward additive approach and the second on the inverse compositional method. As it is customary in iterative optimization, in each iteration the nonlinear objective function is approximated by an alternative expression for which the corresponding optimization is simple. In our case we propose an efficient approximation that leads to a closed form solution (per iteration) which is of low computational complexity, the latter property being particularly strong in our inverse version. The proposed schemes are tested against the Forward Additive Lucas-Kanade and the Simultaneous Inverse Compositional algorithm through simulations. Under noisy conditions and photometric distortions our forward version achieves more accurate alignments and exhibits faster convergence whereas our inverse version has similar performance as the Simultaneous Inverse Compositional algorithm but at a lower computational complexity.     

马尔可夫跳变系统的鲁棒故障检测与时域优化

研究马尔可夫跳变系统(MJS) 鲁棒故障检测滤波器(FDF) 的设计与优化问题. 基于观测器构建残差发生器, 将相应的FDF 设计问题转化为H_∞ 滤波问题, 以LMI 的形式得到并证明了FDF 存在的充分条件及求解方法. 为进一步改善故障检测系统的性能, 采用一种时域优化方法对其进行优化, 并以矩阵Moore-Penrose 逆的形式给出了该优化问题的最优解. 数值仿真表明该方法具有较好的检测效果.     

A stochastic model for heterogeneous computing and its applicationin data relocation scheme development

In a dedicated, mixed-machine, heterogeneous computing (HC) system, an application program may be decomposed into subtasks, then each subtask assigned to the machine where it is best suited for execution. Data relocation is defined as selecting the sources for needed data items. It is assumed that multiple independent subtasks of an application program can be executed concurrently on different machines whenever possible. A theoretical stochastic model for HC Is proposed, in which the computation times of subtasks and communication times for intermachine data transfers can be random variables. The optimization problem for finding the optimal matching, scheduling, and data relocation schemes to minimize the total execution time of an application program is defined based on this stochastic HC model. The global optimization criterion and search space for the above optimization problem are described. It is validated that a greedy algorithm-based approach can establish a local optimization criterion for developing data relocation heuristics. The validation is provided by a theoretical proof based on a set of common assumptions about the underlying HC system and application program. The local optimization criterion established by the greedy approach, coupled with the search space defined for choosing valid data relocation schemes, can help developers of future practical data relocation heuristics     

New Formulation of Dynamic Output Feedback Robust Model Predictive Control with Guaranteed Quadratic Boundedness

The dynamic output feedback robust model predictive controller for a system with both polytopic uncertainty and bounded disturbance is addressed in this paper. This controller utilizes a main optimization problem to find the control law and a simple auxiliary optimization problem to refresh the bounds on the true state. The main optimization problem, which is not necessarily solved at each sampling instant, achieves the near‐optimal solution. The auxiliary optimization, which is solved at each sampling instant, is followed with a simple criterion which determines whether or not to solve the main optimization problem at the next sampling time. By applying the proposed method, the augmented state of the closed‐loop system is guaranteed to converge to the neighborhood of the equilibrium point.     

Optimal nonuniform sampling interval and test-input design for identification of physiological systems from very limited data

Optimal design of test-inputs and sampling intervals in experiments for linear system identification is treated as a nonlinear integer optimization problem. The criterion is a function of the Fisher information matrix, the inverse of which gives a lower bound for the covariance matrix of the parameter estimates. Emphasis is placed on optimum design of nonuniform data sampling intervals when experimental constraints allow only a limited number of discrete-time measurements of the output. A solution algorithm based on a steepest descent strategy is developed and applied to the design of a biologic experiment for estimating the parameters of a model of the dynamics of thyroid hormone metabolism. The effects on parameter accuracy of different model representations are demonstrated numerically, a canonical representation yielding far poorer accuracies than the original process model for nonoptimal sampling schedules, but comparable accuracies when these schedules are optimized. Several objective functions for optimization are compared. The overall results indicate that sampling schedule optimization is a very fruitful approach to maximizing expected parameter estimation accuracies when the sample size is small.     

Numerical validation for an inverse matrix eigenvalue problem

We describe an algorithm with which one can verify solutions of an additive inverse matrix eigenvalue problem. The algorithm is based on Newton's method using a new criterion for terminating the iteration. In addition, it yields tight interval bounds for the solutions of the problem, thus guaranteeing most of their leading digits in a given floating point system.     

A window moving inverse dynamics optimization for biomechanics of motion

The application of musculoskeletal models to estimate muscle and joint reaction forces usually requires optimization strategies, regardless of using inverse or forward dynamics approaches. Most studies combined inverse dynamics and Static Optimization (SO) to solve the redundant muscle force distribution problem. However, the SO does not allow the simulation of time-dependent physiological criteria or of the time-dependent physiological nature of muscles. The Extended Inverse Dynamics (EID), which solves all instants of time simultaneously, was proposed to overcome these limitations of the SO, but the feasibility of this procedure is limited by the size of the optimization problem that can be realistically considered. This work proposes a new method that overcomes the aforementioned limitations of the SO and EID, i.e., that is able to handle time-dependent physiological criteria and has no limitations on the size of the problem to be solved. The proposed procedure, named here Window Moving Inverse Dynamics Optimization (WMIDO), consists in considering a moving window with the size of \(k\) instants of time in which the muscle force distribution problem is solved. The window moves iteratively across all instants of time until the muscle force distribution problem has been solved. The SO, EID, and WMIDO are applied to solve an upper limb abduction in the frontal plane, for which results are widely available in the literature, to demonstrate that similar optimal solutions are obtained for a time-independent physiological criterion if the redundant problem is not too large. Although the WMIDO is not as efficient as the SO for the type of problem tested, it is significantly faster than the EID. Moreover, the WMIDO is able to solve the motion under analysis regardless of the discretization level considered, whereas the EID fails due to memory limitations. Overall, the results show the WMIDO as a viable alternative to the current optimization procedures based on inverse dynamics.     

System shape optimization and stabilization of controlled quasi-linear stochastic systems that operate on an infinite time interval

The necessary conditions in the stabilization and optimization problem for a stationary quasi-linear stochastic system in continuous time, with its matrices depending on a vector parameter to be chosen, i.e., the optimization problem for the system shape, are obtained. An equivalent deterministic problem is stated and a numerical method to solve it using the analytical formula obtained for the criterion gradient, which is the function of a finite number of variables, is proposed. The optimization problem for an output-controlled system is a particular case, sufficient optimality conditions are obtained for it in the case that the complete information of the state is available. Optimality conditions are found for the proportional–integral–derivative controller in the quasi-linear stochastic system. These optimality conditions are applied to the optimal control problem for a small unmanned aerial vehicle moving in a disturbed atmosphere.     

Optimal inner-product angular momentum controllers

An optimization technique is presented to reduce to zero the angular velocities of a spinning object while minimizing a general performance criterion. Closed-form control laws are obtained for a controller structure with a single nonlinear transducer in the feedback loop that employs the square of the Euclidean distance to the origin as an error signal. Consideration is also given to the "inverse problem" of optimal control. Linearization and generalization of the nonlinear plant are discussed.     

Simultaneous identification of damage and input dynamic force on the structure for structural health monitoring

In this paper, we present an approach for simultaneous identification of the system parameters and the input dynamic force time history. The inverse problem associated with the system identification is formulated as an optimization problem and is solved using a newly developed dynamic hybrid adaptive firefly algorithm (DHAFA). A modified version of Tikhonov regularization is employed while solving the inverse problem associated with the force identification in order to improve the quality of the solution. Numerical simulation studies have been carried out by solving three distinct numerical examples. Studies presented in this paper indicate that the proposed algorithm is effective in identifying the system parameters as well as the input dynamic force simultaneously and can be effectively used for structural health monitoring purposes. Convergence studies presented in this paper on the newly developed dynamic hybrid firefly algorithm indicate that the proposed algorithm has better convergence characteristics and can be effectively employed for solving complex nonlinear optimization problems associated with system identification.