Iterative Convex Optimization Algorithm Research Articles

Optimal Trajectory Generation for Intelligent Vehicles in Complex Traffic Based on Iteration Convex Optimization

Intelligent vehicles face considerable challenges in the complex traffic environment since they need to deal with various constraints and elements. This dissertation puts forward a novel trajectory planning framework for intelligent vehicles to generate safe and optimal driving trajectories. First, we design a spatiotemporal occupancy framework to deal with all kinds of elements in the complex driving environment based on the Frenét frame. This framework unifies various constraints on the road in the three-dimensional spatiotemporal representation and clearly describes the collision-free configuration space. Then we use the convex approximation method to construct a time-varying convex feasible region based on the above accurate temporal and spatial description. We formulate the trajectory planning problem as a standard quadratic programming formulation with collision-free and dynamics constraints. Finally, we apply the iterative convex optimization algorithm to solve the quadratic programming problem in the time-varying convex feasible region. Moreover, we design several typical experimental scenarios and have verified that the proposed method has good effectiveness and real-time.

Pattern Synthesis for Dual-Polarized Conformal Arrays via Iterative Convex Optimization

An iterative convex optimization (ICO) algorithm is proposed to solve pattern synthesis problem under the framework of dual-polarized conformal arrays in this paper. The subproblems of shaping main lobe, optimizing side lobe, and suppressing cross-polarization component are summarized as a joint optimization problem. To solve this problem, the nonconvex constraint about main lobe is rewritten as a convex constraint, which will bring error. And an auxiliary phase function is introduced to correct this error alternatively. Due to the deviation between auxiliary phase and real phase of pattern function, a method minimizing the peak of the synthesis error over observation angles is effectively applied to further improve the performance of the method. Numerical examples show good pattern synthesis ability and convergence performance of the ICO method.

Concentric Ring Array Synthesis for Low Side Lobes: An Overview and a Tool for Optimizing Ring Radii and Angle of Rotation

A comprehensive review on the approaches for synthesizing low side lobe concentric ring array (CRA) antennas is given. An Iterative Convex Optimization (ICO) based array layout synthesis technique is proposed for peak side-lobe level (PSLL) minimization over a given circular field-of-view in steerable uniform-amplitude concentric ring array (UA-CRA) antennas. For a given number of rings and number of uniformly-distributed elements in each ring, the ICO algorithm optimizes the ring radii and angle of rotation, with possible constraints on the minimum element separation and largest array size. As compared to the existing UA-CRA synthesis techniques, the proposed method presents unique features as it combines the capability of optimization of angle of rotation of the rings and PSLL minimization for multiple elevation scan angles in a computationally-efficient and easy-to-solve procedure. Through numerical design examples, it is demonstrated how the ICO technique can be effectively used (i) to synthesize sparse UA-CRA topologies generating low PSLL steerable beams, and (ii) to assess and improve the PSLL suppression performance of various known optimization algorithms. Based on the UA-CRA topologies synthesized via competitive methods in the recent literature, a new set of improved array topologies are presented.

Learning stabilizable nonlinear dynamics with contraction-based regularization

We propose a novel framework for learning stabilizable nonlinear dynamical systems for continuous control tasks in robotics. The key contribution is a control-theoretic regularizer for dynamics fitting rooted in the notion of stabilizability, a constraint which guarantees the existence of robust tracking controllers for arbitrary open-loop trajectories generated with the learned system. Leveraging tools from contraction theory and statistical learning in reproducing kernel Hilbert spaces, we formulate stabilizable dynamics learning as a functional optimization with a convex objective and bi-convex functional constraints. Under a mild structural assumption and relaxation of the functional constraints to sampling-based constraints, we derive the optimal solution with a modified representer theorem. Finally, we utilize random matrix feature approximations to reduce the dimensionality of the search parameters and formulate an iterative convex optimization algorithm that jointly fits the dynamics functions and searches for a certificate of stabilizability. We validate the proposed algorithm in simulation for a planar quadrotor, and on a quadrotor hardware testbed emulating planar dynamics. We verify, both in simulation and on hardware, significantly improved trajectory generation and tracking performance with the control-theoretic regularized model over models learned using traditional regression techniques, especially when learning from small supervised datasets. The results support the conjecture that the use of stabilizability constraints as a form of regularization can help prune the hypothesis space in a manner that is tailored to the downstream task of trajectory generation and feedback control. This produces models that are not only dramatically better conditioned, but also data efficient.

Chance-Constrained Trajectory Optimization for Safe Exploration and Learning of Nonlinear Systems

Learning-based control algorithms require data collection with abundant supervision for training. Safe exploration algorithms ensure the safety of this data collection process even when only partial knowledge is available. We present a new approach for optimal motion planning with safe exploration that integrates chance-constrained stochastic optimal control with dynamics learning and feedback control. We derive an iterative convex optimization algorithm that solves an Information-cost Stochastic Nonlinear Optimal Control problem (Info-SNOC). The optimization objective encodes control cost for performance and exploration cost for learning, and the safety is incorporated as distributionally robust chance constraints. The dynamics are predicted from a robust regression model that is learned from data. The Info-SNOC algorithm is used to compute a sub-optimal pool of safe motion plans that aid in exploration for learning unknown residual dynamics under safety constraints. A stable feedback controller is used to execute the motion plan and collect data for model learning. We prove the safety of rollout from our exploration method and reduction in uncertainty over epochs, thereby guaranteeing the consistency of our learning method. We validate the effectiveness of Info-SNOC by designing and implementing a pool of safe trajectories for a planar robot. We demonstrate that our approach has higher success rate in ensuring safety when compared to a deterministic trajectory optimization approach.

Optimization Method for the Energy and Emissions Management of a Hybrid Electric Vehicle with an Exhaust Aftertreatment System

This paper presents a real-time optimization method to compute the fuel-optimal torque split, gear selection and engine on/off command for a Diesel hybrid electric vehicle equipped with an exhaust aftertreatment system. We aim to minimize the amount of fuel consumed, while achieving a charge-sustaining operation and keeping the tailpipe NOx emissions below the legislative limit. We simplify the full vehicle model to facilitate the formulation of a mixed-integer convex problem which is then solved using the proposed iterative convex optimization (ICO) algorithm. We validate the result by comparing it to the globally optimal solution computed using dynamic programming (DP). For the simple model, the ICO algorithm finds the same solution as the DP benchmark. The computation time was reduced from one week for the DP benchmark to 49s for the ICO solution. By comparing the DP solution obtained on the full model with the ICO solution evaluated on the full model, we observe an offset in the solution due to model mismatch, but find that the ICO algorithm captures the qualitative trends of the optimal solution. The proposed algorithm is capable of solving the energy and emissions management problem in real-time, forming the basis for online optimal control.

Efficient Pencil Beam Synthesis in 4-D Antenna Arrays Using an Iterative Convex Optimization Algorithm

A novel iterative convex optimization algorithm is proposed for the efficient synthesis of 4-D antenna arrays in this paper. A general nonconvex programming problem in terms of pencil beam synthesis at the center frequency and the suppression of multiple sidebands with different time schemes is first established. In order to decrease the nonconvexity with respect to equivalent excitations, the nonconvex programming problem is then decomposed into a convex optimization problem at the center frequency and a simplified nonconvex optimization problem at sidebands. Based on the optimized results at the center frequency, an iterative convex optimization algorithm that consists in solving a sequence of convex optimization problems is adopted to solve the nonconvex optimization problem efficiently. Because of the introduction of iterative idea and convex optimization, the proposed method achieves a good tradeoff between the optimization time and the optimality of the solution for the synthesis of 4-D antenna arrays of various scales. Numerical examples of uniformly or nonuniformly spaced 4-D antenna arrays are presented to demonstrate the excellent performance of the proposed algorithm in comparison with those of the previously reported methods.

Phase-Only Control of Peak Sidelobe Level and Pattern Nulls Using Iterative Phase Perturbations

Minimization of the maximum sidelobe level for a given array geometry, amplitude distribution, and nulling sectors by phase-only adjustment of the element coefficients is studied. Nonlinear optimization problem for phase distribution is solved using a novel iterative convex optimization algorithm, which includes mutual coupling effects and exploits small phase perturbations at each step. Superiority of the algorithm in terms of the peak sidelobe level and nulling depth achieved over several optimization methods reported in the most relevant literature is demonstrated in several case studies. Finally, a case study is performed to demonstrate added value of the algorithm for millimeter-wave fifth generation application with phase-only radiation pattern forming.

Heart Rate Variability as a Prognostic Factor for Cancer Survival - A Systematic Review

This paper addresses the problems of robust stability analysis and L1-gain controller synthesis for uncertain impulsive positive systems. First, by employing the idea of impulse interval partitioning, an impulse-time-dependent discretized copositive Lyapunov function is proposed to analyze the robust stability and L1-gain performance of the considered system without control inputs, and several stability conditions and L1-gain criteria are respectively derived. Subsequently, a sufficient condition is formulated for the existence of state-feedback controllers with which not only the positivity and robust uniform asymptotic stability of the resulting closed-loop system are guaranteed, but also a prescribed L1-gain performance is satisfied simultaneously. Furthermore, to make the controller synthesis problem numerically tractable, we propose an iterative convex optimization algorithm to compute the desired controller parameters. Finally, three numerical examples and two realistic examples are presented to show the effectiveness and applicability of the proposed methodology.

Robust stability analysis and controller synthesis for uncertain impulsive positive systems under [formula omitted]-gain performance

This paper addresses the problems of robust stability analysis and L1-gain controller synthesis for uncertain impulsive positive systems. First, by employing the idea of impulse interval partitioning, an impulse-time-dependent discretized copositive Lyapunov function is proposed to analyze the robust stability and L1-gain performance of the considered system without control inputs, and several stability conditions and L1-gain criteria are respectively derived. Subsequently, a sufficient condition is formulated for the existence of state-feedback controllers with which not only the positivity and robust uniform asymptotic stability of the resulting closed-loop system are guaranteed, but also a prescribed L1-gain performance is satisfied simultaneously. Furthermore, to make the controller synthesis problem numerically tractable, we propose an iterative convex optimization algorithm to compute the desired controller parameters. Finally, three numerical examples and two realistic examples are presented to show the effectiveness and applicability of the proposed methodology.

Improved results on [formula omitted] model reduction for continuous-time linear systems over finite frequency ranges

This paper revisits the H∞ model reduction problem for continuous-time linear systems over finite frequency ranges. Given an asymptotically stable system, our goal is to find a stable reduced-order system in such a way that the error of the transfer functions between the original system and the reduced-order one is bounded over a finite frequency range. By virtue of the generalized Kalman–Yakubovich–Popov (GKYP) Lemma, we first establish necessary and sufficient characterizations for this problem in terms of linear matrix inequalities (LMIs). For the low- and mid-frequency cases, through introducing a non-conservative multiplier and resorting to the projection lemma, the reduced-order system matrices are decoupled with the matrix variables from the GKYP Lemma. Then, by introducing a new diagonal matrix variable and based on congruence transformation, the reduced-order system matrices are further decoupled with the matrix variable induced by the projection lemma and can be parameterized by a new matrix variable. The results are extended to the high-frequency case without the use of projection lemma to reduce the conservatism. Moreover, an iterative convex optimization algorithm is developed to solve the conditions. Finally, we demonstrate via numerical examples that our method can achieve much smaller approximation error than existing results.

On static output‐feedback stabilization for multi‐input multi‐output positive systems

SummaryThis paper revisits the static output‐feedback stabilization problem for positive systems. We first point out that for a class of positive systems whose output matrix has a particular row echelon form, this problem can be completely solved via linear programming. By duality, the result is also valid when the column echelon form of the input matrix has a particular structure. Along this line, by augmenting the output matrix as well as the feedback gain matrix, an iterative convex optimization algorithm is developed for the more general case. Finally, we show that the proposed method has advantages over existing works via several numerical examples. Copyright © 2014 John Wiley & Sons, Ltd.

Robust Registration by Rank Minimization for Multiangle Hyper/Multispectral Remotely Sensed Imagery

Multiangle images are acquired over roughly the same earth surface from different angles, and accurate image registration is a key prerequisite for their application. In this paper, we propose a robust registration method by rank minimization (RRRM) for multiangle hyper/multispectral remotely sensed imagery (MA-HSI-MSI). First, the low-rank structure of the MA-HSI-MSI is exploited and utilized as the registration constraint, thus recasting the image registration problem as searching for an optimal set of transformations, such that the matrix of the transformed images can reach its minimum rank. Second, a patch-based registration scheme is adopted to solve the problem of inconsistent geometric distortion over the entire image, taking the homography model as the local transformation. An iterative convex optimization algorithm is then used to solve the rank minimization-based image registration model for each image patch. Finally, all the transformed patches are used to synthesize the final registration image. The experimental results demonstrate that the proposed low-rank registration method works effectively for CHRIS/Proba imagery and WorldView-2 imagery.

H ∞ model reduction for discrete‐time positive systems with inhomogeneous initial conditions

SUMMARYThis paper addresses the H ∞ model reduction problem of discrete‐time positive linear systems with inhomogeneous initial conditions. For an asymptotically stable positive system with non‐zero initial condition, our goal is to approximate it by a reduced‐order initial‐valued positive system without introducing significant error. We establish a necessary and sufficient condition for the existence of a desired reduced‐order model such that the output error between the original system and the reduced‐order one is bounded by a weighted sum of the magnitude of the input and that of the initial condition. Moreover, based on congruent transformation and the dual form of bounded real lemma, several equivalent conditions are derived in terms of LMIs and an iterative convex optimization algorithm is developed accordingly. Finally, an illustrative example is presented to show the effectiveness of the proposed methods. Copyright © 2013 John Wiley & Sons, Ltd.