In this study, a noniterative, convex programming-based optimal guidance is proposed to address field-of-view and acceleration constraints while achieving terminal impact angles. To circumvent the problems of successi...
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In this study, a noniterative, convex programming-based optimal guidance is proposed to address field-of-view and acceleration constraints while achieving terminal impact angles. To circumvent the problems of successive convex programming, such as convergence stability and local optimality, the original guidance problem is reformulated as a quadratic programming problem by employing a limited approximation of look angle. Furthermore, a range-to-go weighted cost function is utilized, which allows the acceleration profile to be shaped based on the gain of the weighting function. A pseudo-spectral method is adopted in the transcription process due to its high solution accuracy. The proposed method rapidly provides optimal guidance solutions without iterations and convergence issues, which makes it suitable for real-time implementation. The performance and utility of the proposed method are demonstrated via extensive simulations.
This paper investigates the robust fuel-optimal guidance problem for powered descent landing under uncertainty. A robust optimal control problem (OCP) with stochastic dynamics and constraints is first constructed to e...
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This paper investigates the robust fuel-optimal guidance problem for powered descent landing under uncertainty. A robust optimal control problem (OCP) with stochastic dynamics and constraints is first constructed to ensure both optimality and safety. The polynomial chaos expansion (PCE)-based uncertainty quantification technique is then employed to convert the stochastic OCP into a high-dimensional deterministic OCP, which, while tractable, involves a large number of decision variables and is computationally intensive. To mitigate this issue, the dynamics are convexified within the model predictive convex programming (MPCP) framework, reducing the number of decision variables by establishing the sensitivity relationship between state and control corrections. Furthermore, convexification techniques including lossless convexification and successive convexification are applied to convexify the nonlinear inequality constraints. To enhance computational efficiency, a dimension reduction method is also introduced. After solving the robust OCP through convex optimization, a closed-loop guidance algorithm based on receding horizon strategy is proposed to address navigational errors. Numerical simulations demonstrate the advantages of this guidance algorithm.
In this paper a minimization problem with convex objective function Subject to a separable convex inequality constraint "=" constraint and bounds on the variables are also considered. Numerical illustration ...
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In this paper a minimization problem with convex objective function Subject to a separable convex inequality constraint "<=" and bounded variables (box constraints) is considered. We propose an iterative algorithm for solving this problem based oil line search and convergence of this algorithm is proved. At each iteration, a separable convex programming problem with the same constraint set is solved using Karush-Kuhn-Tucker conditions. convex minimization problems subject to linear equality/ linear inequality ">=" constraint and bounds on the variables are also considered. Numerical illustration is included in Support of theory.
The capacity of 1-D constraints is given by the entropy of a corresponding stationary maxentropic Markov chain. Namely, the entropy is maximized over a set of probability distributions, which is defined by some linear...
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The capacity of 1-D constraints is given by the entropy of a corresponding stationary maxentropic Markov chain. Namely, the entropy is maximized over a set of probability distributions, which is defined by some linear equalities and inequalities. In this paper, certain aspects of this characterization are extended to 2-D constraints. The result is a method for calculating an upper bound on the capacity of 2-D constraints. The key steps are as follows: The maxentropic stationary probability distribution on square configurations is considered;set of linear equalities and inequalities is derived from this stationarity;the result is then a convex program, which can be easily solved numerically. Our method improves upon previous upper bounds for the capacity of the 2-D "no isolated bits" constraint, as well as certain 2-D RLL constraints.
We propose a formulation for nonlinear recurrent models that includes simple parametric models of recurrent neural networks as a special case. The proposed formulation leads to a natural estimator in the form of a con...
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We propose a formulation for nonlinear recurrent models that includes simple parametric models of recurrent neural networks as a special case. The proposed formulation leads to a natural estimator in the form of a convex program. We provide a sample complexity for this estimator in the case of stable dynamics, where the nonlinear recursion has a certain contraction property, and under certain regularity conditions on the input distribution. We evaluate the performance of the estimator by simulation on synthetic data. These numerical experiments also suggest the extent at which the imposed theoretical assumptions may be relaxed.
In this paper we consider the H-2-control problem for the class of discrete-time linear systems with parameters subject to markovian jumps using a convex programming approach. We generalize the definition of the H-2 n...
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In this paper we consider the H-2-control problem for the class of discrete-time linear systems with parameters subject to markovian jumps using a convex programming approach. We generalize the definition of the H-2 norm from the deterministic case to the markovian jump case and set a link between this norm and the observability and controllability gramians. Conditions for existence and derivation of a mean square stabilizing controller for a markovian jump linear system using convex analysis are established. The main contribution of the paper is to provide a convex programming formulation to the H-2-control problem, so that several important cases, to our knowledge not analysed in previous work, can be addressed. Regarding the transition matrix P = [p(ij)] for the Markov chain, two situations are considered: the case in which it is exactly known, and the case in which it is not exactly known but belongs to an appropriated convex set. Regarding the state variable and the jump variable, the cases in which they may or may not be available to the controller are considered. If they are not available, the H-2-control problem can be written as an optimization problem over the intersection of a convex set and a set defined by nonlinear real-valued functions. These nonlinear constraints exhibit important geometrical properties, leading to cutting-plane-like algorithms. The theory is illustrated by numerical simulations.
This paper devises an optimization framework for efficient energy management and components sizing of a plug-in fuel cell urban logistics vehicle. Based on the propulsion system structure, fuel cell system model, and ...
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This paper devises an optimization framework for efficient energy management and components sizing of a plug-in fuel cell urban logistics vehicle. Based on the propulsion system structure, fuel cell system model, and convex battery health model, a convex programming problem is formulated to simultaneously optimize both the control decision and parameters of power sources, including a fuel cell pack and a battery pack. This paper seeks to minimize a summation of energy cost and power sources cost, while satisfying vehicle power demand and battery health requirements. Considering different drive cycles, the optimal parameters and energy cost are systematically investigated. As a result, the optimal battery rated power and energy capacity are about 54 kW and 29 kWh, respectively, which are not affected by different drive cycles, given an electric-only range between 40 km and 60 km. Finally, based on the developed convex programming control law and optimal parameters, we examine the power distribution of the plug-in fuel cell urban logistics vehicle with different hydrogen prices, which significantly influences the vehicle's fuel economy.
Clustering is a fundamental task in data analysis, and spectral clustering has been recognized as a promising approach to it. Given a graph describing the relationship between data, spectral clustering explores the un...
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Clustering is a fundamental task in data analysis, and spectral clustering has been recognized as a promising approach to it. Given a graph describing the relationship between data, spectral clustering explores the underlying cluster structure in two stages. The first stage embeds the nodes of the graph in real space, and the second stage groups the embedded nodes into several clusters. The use of the k-means method in the grouping stage is currently standard practice. We present a spectral clustering algorithm that uses convex programming in the grouping stage and study how well it works. This algorithm is designed based on the following observation. If a graph is well-clustered, then the nodes with the largest degree in each cluster can be found by computing an enclosing ellipsoid of the nodes embedded in real space, and the clusters can be identified by using those nodes. We show that, for well-clustered graphs, the algorithm can find clusters of nodes with minimal conductance. We also give an experimental assessment of the algorithm's performance.
Given a finite number of closed convex sets whose algebraic representation is known, we study the problem of finding the minimum of a convex function on the closure of the convex hull of the union of those sets. We de...
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Given a finite number of closed convex sets whose algebraic representation is known, we study the problem of finding the minimum of a convex function on the closure of the convex hull of the union of those sets. We derive an algebraic characterization of the feasible region in a higher-dimensional space and propose a solution procedure akin to the interior-point approach for convex programming.
Duality results are established in convex programming with the set-inclusive constraints studied by Soyster. The recently developed duality theory for generalized linear programs by Thuente is further generalized and ...
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Duality results are established in convex programming with the set-inclusive constraints studied by Soyster. The recently developed duality theory for generalized linear programs by Thuente is further generalized and also brought into the framework of Soyster's theory. convex programming with set-inclusive constraints is further extended to fractional programming.
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