A globally convergent estimator for n-frequencies

In this paper, we propose a solution to the well-known problem of ensuring a simultaneous globally convergent online estimation of the state and the frequencies of a sinusoidal signal composed of n sinusoidal terms. We present an estimator which guarantees global boundedness and convergence of both the state estimation and the frequency estimation for all initial conditions and frequency values     

A globally convergent frequency estimator

Online estimation of the frequency of a sinusoidal signal is a classical problem in systems theory that has many practical applications. In this paper the authors provide a solution to the problem of ensuring a globally convergent estimation. More specifically, they propose a new adaptive notch filter whose dynamic equations exhibit the following remarkable features: 1) all signals are globally bounded and the estimated frequency is asymptotically correct for all initial conditions and all frequency values; 2) the authors obtain a simple tuning procedure for the estimator design parameters, which trades-off the adaptation tracking capabilities with noise sensitivity, ensuring (exponential) stability of the desired orbit; and 3) transient performance is considerably enhanced, even for small or large frequencies, as witnessed by extensive simulations. To reveal some of the stability-instability mechanisms of the existing algorithms and motivate our modifications the authors make appeal to a novel nonlinear (state-dependent) time scaling. The main advantage of working in the new time scale is that they remove the coupling between the parameter update law and the filter itself, decomposing the system into a feedback form where the required modifications to ensure stability become apparent. Even though they limit their attention here to the simplest case of a single constant frequency without noise the algorithm is able to track time-varying frequencies, preserve local stability in the presence of multiple sinusoids, and is robust with respect to noise     

A globally optimal minimax solution for spectral overbounding andfactorization

In this paper, an algorithm is introduced to find a minimum phase transfer function of specified order whose magnitude “tightly” overbounds a specified real-valued nonparametric function of frequency. This method has direct application to transforming nonparametric uncertainty bounds (available from system identification experiments and/or plant modeling) into parametric representations required for modern robust control design software (i.e., a minimum-phase transfer function multiplied by a norm-bounded perturbation)     

A globally convergent algorithm for the optimal constant output feedback problem

A dual version of the Levine-Athans algorithm for solving the optimal constant output feedback gain for continuous-time systems is studied. Global convergence of the procedure to a stationary point of the loss function is proved. A global convergence property of the Levine-Athans algorithm is also obtained.     

Efficient algorithms for globally optimal trajectories

We present serial and parallel algorithms for solving a system of equations that arises from the discretization of the Hamilton-Jacobi equation associated to a trajectory optimization problem of the following type. A vehicle starts at a prespecified point x_o and follows a unit speed trajectory x(t) inside a region in ℛ^m until an unspecified time T that the region is exited. A trajectory minimizing a cost function of the form ∫₀^T r(x(t))dt+q(x(T)) is sought. The discretized Hamilton-Jacobi equation corresponding to this problem is usually solved using iterative methods. Nevertheless, assuming that the function r is positive, we are able to exploit the problem structure and develop one-pass algorithms for the discretized problem. The first algorithm resembles Dijkstra's shortest path algorithm and runs in time O(n log n), where n is the number of grid points. The second algorithm uses a somewhat different discretization and borrows some ideas from a variation of Dial's shortest path algorithm (1969) that we develop here; it runs in time O(n), which is the best possible, under some fairly mild assumptions. Finally, we show that the latter algorithm can be efficiently parallelized: for two-dimensional problems and with p processors, its running time becomes O(n/p), provided that p=O(√n/log n)     

Rule-based modeling: fast construction and optimal manipulation

This paper considers the problem of modeling an unknown system by a rule-based model constructed from measured data. In particular, we address two fundamental issues associated with the rule-based modeling: rule-base construction and rule-base manipulation. A two-step approach consisting of a principal and a refining algorithm has been suggested to extract rules from the available data set. Starting from the notion of product space clustering, we have developed three principal algorithms in which fuzzy concepts and competitive learning are utilized. A particular attention is paid to enabling the algorithms to have self-organizing capability and real-time applicability. Two algorithms have been presented for manipulating the obtained rule-base with novel data, one being a direct application of a fuzzy control algorithm and the other being an optimal algorithm in the sense of least square error with respect to an appropriately chosen cost function. Simulation results on three examples taken from function approximation, time-series prediction, and nonlinear dynamical modeling are given     

Modeling basal ganglia for understanding Parkinsonian reaching movements

We present a computational model that highlights the role of basal ganglia (BG) in generating simple reaching movements. The model is cast within the reinforcement learning (RL) framework with correspondence between RL components and neuroanatomy as follows: dopamine signal of substantia nigra pars compacta as the temporal difference error, striatum as the substrate for the critic, and the motor cortex as the actor. A key feature of this neurobiological interpretation is our hypothesis that the indirect pathway is the explorer. Chaotic activity, originating from the indirect pathway part of the model, drives the wandering, exploratory movements of the arm. Thus, the direct pathway subserves exploitation, while the indirect pathway subserves exploration. The motor cortex becomes more and more independent of the corrective influence of BG as training progresses. Reaching trajectories show diminishing variability with training. Reaching movements associated with Parkinson's disease (PD) are simulated by reducing dopamine and degrading the complexity of indirect pathway dynamics by switching it from chaotic to periodic behavior. Under the simulated PD conditions, the arm exhibits PD motor symptoms like tremor, bradykinesia and undershooting. The model echoes the notion that PD is a dynamical disease.     

A branch-and-bound algorithm for globally optimal camera pose and focal length

This paper considers the problem of finding the global optimum of the camera rotation, translation and the focal length given a set of 2D–3D point pairs. The global solution is obtained under the L-infinity optimality by a branch-and-bound algorithm. To obtain the goal, we firstly extend the previous branch-and-bound formulation and show that the image space error (pixel distance) may be used instead of the angular error. Then, we present that the problem of camera pose plus focal length given the rotation is a quasi-convex problem. This provides a derivation of a novel inequality for the branch-and-bound algorithm for our problem. Finally, experimental results with synthetic and real data are provided.     

Minimum acceleration criterion with constraints implies bang-bang control as an underlying principle for optimal trajectories of arm reaching movements

Rapid arm-reaching movements serve as an excellent test bed for any theory about trajectory formation. How are these movements planned? A minimum acceleration criterion has been examined in the past, and the solution obtained, based on the Euler-Poisson equation, failed to predict that the hand would begin and end the movement at rest (i.e., with zero acceleration). Therefore, this criterion was rejected in favor of the minimum jerk, which was proved to be successful in describing many features of human movements. This letter follows an alternative approach and solves the minimum acceleration problem with constraints using Pontryagin's minimum principle. We use the minimum principle to obtain minimum acceleration trajectories and use the jerk as a control signal. In order to find a solution that does not include nonphysiological impulse functions, constraints on the maximum and minimum jerk values are assumed. The analytical solution provides a three-phase piecewise constant jerk signal (bang-bang control) where the magnitude of the jerk and the two switching times depend on the magnitude of the maximum and minimum available jerk values. This result fits the observed trajectories of reaching movements and takes into account both the extrinsic coordinates and the muscle limitations in a single framework. The minimum acceleration with constraints principle is discussed as a unifying approach for many observations about the neural control of movements.     

Model predictive control for fast reaching in clutter

A key challenge for haptically reaching in dense clutter is the frequent contact that can occur between the robot’s arm and the environment. We have previously used single-time-step model predictive control (MPC) to enable a robot to slowly reach into dense clutter using a quasistatic mechanical model. Rapid reaching in clutter would be desirable, but entails additional challenges due to dynamic phenomena that can lead to higher forces from impacts and other types of contact. In this paper, we present a multi-time-step MPC formulation that enables a robot to rapidly reach a target position in dense clutter, while regulating whole-body contact forces to be below a given threshold. Our controller models the dynamics of the arm in contact with the environment in order to predict how contact forces will change and how the robot’s end effector will move. It also models how joint velocities will influence potential impact forces. At each time step, our controller uses linear models to generate a convex optimization problem that it can solve efficiently. Through tens of thousands of trials in simulation, we show that with our dynamic MPC a simulated robot can, on average, reach goals 1.4 to 2 times faster than our previous controller, while attaining comparable success rates and fewer occurrences of high forces. We also conducted trials using a real 7 degree-of-freedom (DoF) humanoid robot arm with whole-arm tactile sensing. Our controller enabled the robot to rapidly reach target positions in dense artificial foliage while keeping contact forces low.     

Synthesis of globally optimal controllers for robust performance tounstructured uncertainty

This paper solves the problem of synthesis of controllers achieving globally optimal robust performance against unstructured time-varying and/or nonlinear uncertainty. The performance measure considered is the infinity-to-infinity induced norm of a system's transfer function. The solution utilizes sensitivity analysis of linear programming and the theory of parametric programming     

A fast algorithm for constructing nearly optimal prefix codes

Huffman algorithm allows for constructing optimal prefix‐codes with O(n·logn) complexity. As the number of symbols ngrows, so does the complexity of building the code‐words. In this paper, a new algorithm and implementation are proposed that achieve nearly optimal coding without sorting the probabilities or building a tree of codes. The complexity is proportional to the maximum code length, making the algorithm especially attractive for large alphabets. The focus is put on achieving almost optimal coding with a fast implementation, suitable for real‐time compression of large volumes of data. A practical case example about checkpoint files compression is presented, providing encouraging results. Copyright © 2015 John Wiley & Sons, Ltd.     

The optimal reduced-order estimator for systems with singularmeasurement noise

The optimal reduced-order estimator is completely characterized by necessary conditions, resulting from the optimal projection equations. The solution consists of one Riccati equation and two Lyapunov equations coupled by two projections. Explicit expressions for all of the estimator parameters are given. The relation between the reduced-order singular estimator and the full-order optimal singular estimator (which is of reduced order itself) is investigated. It is shown that under certain conditions the optimal estimator is recovered from the reduced-order estimator     

A three-dimensional dynamic posture prediction model for in-vehicle seated reaching movements: development and validation

A three-dimensional dynamic posture prediction model for simulating in-vehicle reaching movements is presented. The model employs a four-segment 7-degrees-of-freedom linkage structure to represent the torso, clavicle and right extremity. It relies on an optimization-based differential inverse kinematics to estimate a set of four weighting parameters that quantify a timeconstant, inter-segment motion apportionment strategy. In the development 100 seated reaching movements performed by 10 subjects towards five in-vehicle targets were modelled, resulting in 100 sets of weighting Statistical analysis was then conducted to relate these parameters to and individual attributes. In the validation phase, the generalized model, parameter values statistically synthesized, was applied to novel data sets 700 different reaching movements (towards different targets and/or by subjects). The results demonstrated the model's ability to generate close in prediction: the overall mean time-averaged error in joint angle 5.2°, and the median was 4.7°, excluding reaches towards two extreme targets which modelling errors were excessive). The model's general success in and its unique characteristics led to implications with regard to the and underlying control strategies of human reaching movements.     

Learning of a controller for non-recurring fast movements

In this paper a learning method is described which enables a conventional industrial robot to accurately execute the teach-in path in the presence of dynamical effects and high speed. After training the system is capable of generating positional commands that in combination with the standard robot controller lead the robot along the desired trajectory. The mean path deviations are reduced to a factor of 20 for our test configuration. For low speed motion the learned controllers' accuracy is in the range of the resolution of the positional encoders. The learned controller does not depend on specific trajectories. It acts as a general controller that can be used for non-recurring tasks as well as for sensor-based planned paths. For repetitive control tasks accuracy can be even increased. Such improvements are caused by a three level structure estimating a simple process model, optimal a posteriori commands, and a suitable feedforward controller, the latter including neural networks for the representation of nonlinear behaviour. The learning system is demonstrated in experiments with a Manutec R2 industrial robot. After training with only two sample trajectories the learned control system is applied to other totally different paths which are executed with high precision as well.     

A novel adaptive control for reaching movements of an anthropomorphic arm driven by pneumatic artificial muscles

Pneumatic artificial muscle is widely used since it has the advantage including simple structure, lightweight, force controllable, compliance and so on. In this paper, a two-link anthropomorphic arm is constructed by pneumatic artificial muscles for the upper-limb rehabilitation training. In order to assist impaired upper-limb patients to achieve various training, the anthropomorphic arm should realize flexible human reaching movements. Due to frictions and model uncertainties of the anthropomorphic arm system, an adaptive fuzzy backstepping control is proposed to ensure the stability and the adaptivity during the motion. The control method is proved by Lyapunov asymptotic stability and is verified by numerical simulations. Furthermore, experiments are performed and results demonstrate that the proposed control method is efficient and robust.     

大规模城市可计算模型快速构建方法研究

为了给数值模拟计算提供大规模城市的可计算模型,需要具备面向大空间尺度、海量数据、频繁更新的城市的快速可计算建模能力。但是,由于数据采集过程中存在的误差,以及模型处理所做的必要的简化操作,导致直接生成的数字城市模型中存在大量非闭合、相接、相交、悬空等CAD模型缺陷,使得城市模型不可用于数值模拟。而采用商用软件直接修复这些缺陷的代价过高。为此,提出面向大规模城市可计算模型的快速构建方法。通过分析LoD1城市模型中所涉及的CAD模型缺陷,提出了需满足的可计算条件和对应的处理方法。 提出的方法能够直接生成不存在CAD模型缺陷的城市可计算模型。为了提高可计算处理的效率,还提出了面向大规模城市的图形快速检索算法。实验表明,构建710 km2、30余万栋建筑、217万面片的可计算模型仅需约25 min,满足了在大规模城市上进行数值模拟的需求。     

Extensions to the repetitive branch and bound algorithm for globally optimal clusterwise regression

A branch and bound strategy is proposed for solving the clusterwise regression problem, extending Brusco's repetitive branch and bound algorithm (RBBA). The resulting strategy relies upon iterative heuristic optimization, new ways of observation sequencing, and branch and bound optimization of a limited number of ending subsets. These three key features lead to significantly faster optimization of the complete set and the strategy has more general applications than only for clusterwise regression. Additionally, an efficient implementation of incremental calculations within the branch and bound search algorithm eliminates most of the redundant ones. Experiments using both real and synthetic data compare the various features of the proposed optimization algorithm and contrasts them against a benchmark mixed logical-quadratic programming formulation optimized by CPLEX. The results indicate that all components of the proposed algorithm provide significant improvements in processing times, and, when combined, generally provide the best performance, significantly outperforming CPLEX.     

A three-dimensional dynamic posture prediction model for simulating in-vehicle seated reaching movements: development and validation

A three-dimensional dynamic posture prediction model for simulating in-vehicle seated reaching movements is presented. The model employs a four-segment 7-degrees-of-freedom linkage structure to represent the torso, clavicle and right upper extremity. It relies on an optimization-based differential inverse kinematics approach to estimate a set of four weighting parameters that quantify a time-constant, inter-segment motion apportionment strategy. In the development phase, 100 seated reaching movements performed by 10 subjects towards five typical in-vehicle targets were modelled, resulting in 100 sets of weighting parameters. Statistical analysis was then conducted to relate these parameters to target and individual attributes. In the validation phase, the generalized model, with parameter values statistically synthesized, was applied to novel data sets containing 700 different reaching movements (towards different targets and/or by different subjects). The results demonstrated the model's ability to generate close representations in prediction: the overall mean time-averaged error in joint angle was 5.2 degrees, and the median was 4.7 degrees, excluding reaches towards two extreme targets (for which modelling errors were excessive). The model's general success in prediction and its unique characteristics led to implications with regard to the performance and underlying control strategies of human reaching movements.