Minimum Energy Constraints Research Articles

Formation control for networked multiagent systems with a minimum energy constraint

Minimum-energy formation achievement problems for networked multiagent systems are investigated, where information networks with leaderless and leader-follower structures are respectively addressed and information networks are randomly switching. The critical feature of this work is that the energy constraint is minimum in the sense of the linear matrix inequality, but limited-budget control and guaranteed-cost control cannot realize a minimum-energy formation. Firstly, the leaderless minimum-energy formation control problem is converted into an asymptotic stability one via a nonsingular transformation and state space decomposition, and based on linear matrix inequality techniques, sufficient conditions for analysis and design of leaderless minimum-energy formation achievement are proposed, respectively, which can be solved by the generalized eigenvalue method. Then, main results of minimum-energy formation achievement of leaderless networked multiagent systems are extended leader-follower networked multiagent systems, where the asymmetric property of the leader-follower information network is well dealt with by two nonsingular transformations. Finally, two simulation examples are shown to verify the main results for minimum-energy formation achievements of leaderless and leader-follower networked multiagent systems, respectively.

Dictionary learning of sound speed profiles.

To provide constraints on the inversion of ocean sound speed profiles (SSPs), SSPs are often modeled using empirical orthogonal functions (EOFs). However, this regularization, which uses the leading order EOFs with a minimum-energy constraint on the coefficients, often yields low resolution SSP estimates. In this paper, it is shown that dictionary learning, a form of unsupervised machine learning, can improve SSP resolution by generating a dictionary of shape functions for sparse processing (e.g., compressive sensing) that optimally compress SSPs; both minimizing the reconstruction error and the number of coefficients. These learned dictionaries (LDs) are not constrained to be orthogonal and thus, fit the given signals such that each signal example is approximated using few LD entries. Here, LDs describing SSP observations from the HF-97 experiment and the South China Sea are generated using the K-SVD algorithm. These LDs better explain SSP variability and require fewer coefficients than EOFs, describing much of the variability with one coefficient. Thus, LDs improve the resolution of SSP estimates with negligible computational burden.

Dictionary learning of acoustic sound speed profiles

Inversion for true ocean acoustic sound speed profiles (SSPs) is generally a non-linear and underdetermined problem. Traditional regularization methods model SSPs as a summation of leading-order empirical orthogonal functions (EOFs), with a minimum-energy constraint on coefficients. However, this often provides low resolution estimates of ocean SSPs. Sparse processing methods (e.g., compressive sensing) yield high resolution reconstruction of signals from few observations, provided few coefficients (of many) explain the observations. Using dictionary learning techniques, an overcomplete basis or dictionary of shape functions, which represent ocean SSPs using a minimum number of coefficients, is learned from a training set of SSPs. Learned dictionaries, which are not constrained to be orthogonal, optimally fit the distribution of possible ocean SSPs. Thus, each dictionary entry is informative to ocean SSP variability whereas EOFs become less informative for increasing order. It has been found that these learned dictionaries largely explain the variability of ocean SSPs using as few as one coefficient. Thus, in addition to improving the resolution of SSP estimates, learned dictionaries can improve the robustness of SSP inversion by significantly reducing the parameter search space.

Hardy Variation Framework for Restoration of Weather Degraded Images

Images captured in fog conditions often suffer from weather of poor visibility which fades the colors and reduces the contrast in the scene. This paper proposes a novel regularization method which utilizes space transformation in order to restore the hidden scene with high dynamic range and enhanced edge information. In order to efficiently improve the visualization, the proposed method is built upon contrast stretching which can obtain better estimation map as well as solve the problem. Using minimum energy constraints, the algorithm recovers scene albedo on a number of haze images. Experimental results show that the method effectively achieves accurate and true representation.

Shielded resistive electromagnets of arbitrary surface geometry using the boundary element method and a minimum energy constraint

Eddy currents are generated in MR by the use of rapidly switched electromagnets, resulting in time varying and spatially varying magnetic fields that must be either minimized or corrected. This problem is further complicated when non-cylindrical insert magnets are used for specialized applications. Interruption of the coupling between an insert coil and the MR system is typically accomplished using active magnetic shielding. A new method of actively shielding insert gradient and shim coils of any surface geometry by use of the boundary element method for coil design with a minimum energy constraint is presented. This method was applied to shield x- and z-gradient coils for two separate cases: a traditional cylindrical primary gradient with cylindrical shield and, to demonstrate its versatility in surface geometry, the same cylindrical primary gradients with a rectangular box-shaped shield. For the cylindrical case this method produced shields that agreed with analytic solutions. For the second case, the rectangular box-shaped shields demonstrated very good shielding characteristics despite having a different geometry than the primary coils.

On control of linear systems with time lags

The terminal control of a general time invariant linear system with time lags has been studied in a variety of situations by means of the technique of dynamic programming. Optimum control laws, satisfying a minimum energy constraint are explicitly derived under each of the following assumptions concerning the noise in the system: noise free, noise generated by a Markov source, noise whose statistics are partially unknown, and worst case or competitive disturbances.