PAPERS IN CDC
최성준
2013-12-24
DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING
SEOUL NATIONAL UNIVERSITY
PAPER LIST
CPSLAB (http://cpslab.snu.ac.kr)
1. A Bayesian Nonparametric Approach to Adaptive Control using
Gaussian Processes
2. Nonparametric Adaptive Control using Gaussian processes with
Online Hyper-parameter Estimation
3. Feedback Control Law Generation for Safety Controller Synthesis
4. Nonlinear Compressive Particle Filtering
5. Motion Planning in Crowds using Statistical Model Checking to
Enhance the Social Force Model
6. Inverse Optimal control for Deterministic Continuous-time
nonlinear Systems
7. Imputing a Convex Objective Function
Sungjoon Choi
Papers in CDC
2
A BAYESIAN NONPARAMETRIC APPROACH TO ADAPTIVE CONTROL USING
GAUSSIAN PROCESSES
CPSLAB (http://cpslab.snu.ac.kr)
 Model Reference Adaptive Control (MRAC)
 Approximate Model Inversion Based MRAC (AMI-MRAC)
 𝑥1 𝑡 = 𝑥2 𝑡
 𝑥2 𝑡 = 𝑓 𝑥 𝑡 + 𝑏 𝑥 𝑡 𝛿 𝑡
 Given 𝜈, a control command 𝛿 can be computed
 𝛿 = 𝑏 −1 𝑥
𝜈−𝑓 𝑥
 𝑥2 = 𝜈 𝑧 + ∆ 𝑧 with ∆ 𝑧 = 𝑓 𝑥 − 𝑓 𝑥 + 𝑏 𝑥 − 𝑏 𝑥
𝛿
 Model ∆ 𝑧 using Gaussian Process Regression
 ∆ 𝑧 ~𝐺𝑃 𝑚 𝑧 , 𝑘 𝑧, 𝑧′
 It is called MRAC-GP.
Sungjoon Choi
Papers in CDC
3
NONPARAMETRIC ADAPTIVE CONTROL USING GAUSSIAN PROCESSES WITH
ONLINE HYPER-PARAMETER ESTIMATION
CPSLAB (http://cpslab.snu.ac.kr)
 Methods for learning hyper-parameters online in GP-MRAC.

𝛿
log 𝑃
𝛿𝜃𝑗
1
2
𝑦|𝜃, 𝑍 = 𝑡𝑟
𝑎𝑎𝑇 − Σ −1
𝛿Σ
𝛿𝜃𝑗
 where, 𝑎 = Σ𝑧−1 𝑦
 Subset of Data methods
 Place kernels at a set of budgeted active basis vector set 𝐵𝑉 by find the
vector with biggest KL divergence in a greedy manner.
 Implement gradient-based update rule by assuming new
measurements are independent of each other.
 log 𝑃 𝑦|𝑍, 𝜃 ≈
Sungjoon Choi
𝑖∉|𝐵𝑉| log 𝑃
𝑦𝑍 , 𝑦𝑖 |𝑍, 𝑍𝑖 , 𝜃
Papers in CDC
4
FEEDBACK CONTROL LAW GENERATION FOR SAFETY CONTROLLER SYNTHES
CPSLAB (http://cpslab.snu.ac.kr)
 Implement controller based in the reference input obtained from
human playing a simulator of the plant.
 Used piecewise affine system identification techniques to
generate a feedback control law.
Sungjoon Choi
Papers in CDC
5
NONLINEAR COMPRESSIVE PARTICLE FILTERING
CPSLAB (http://cpslab.snu.ac.kr)
 Traditional compressive sensing
min 𝑥
𝑥
𝑠. 𝑡. 𝑦 = 𝐴𝑥
0
 Nonlinear compressive sensing
𝑦 = 𝐴𝑥 2 , 𝑦 ∈ 𝑅𝑁 , 𝐴 ∈ 𝐶 𝑁×𝑛 , 𝑥 ∈ 𝐶 𝑛
 X-ray crystallography, diffraction image, ... , phase retrieval problem
 Steps
 Initialization
 Propagate the predictive distribution
 Compute a particle approximation at 𝑡 = 𝑡 + 1
 Add Elements to the Support
 Update support 𝑠 𝑡 using likelihood thresholding
 Remove Elements from the Support
 based on the distance from the mean of particles
 Update the predictive distribution
Sungjoon Choi
Papers in CDC
6
MOTION PLANNING IN CROWDS USING STATISTICAL MODEL CHECKING TO
ENHANCE THE SOCIAL FORCE MODEL
CPSLAB (http://cpslab.snu.ac.kr)
 Sampling based method to cover an intractably large configuration space.
 Temporal logic & Statistical model checking
 Social force model
𝑝ℎ
 𝑓𝑖 = Σ𝑗≠𝑖 𝑓𝑖𝑗𝑠𝑜𝑐 + 𝑓𝑖𝑗𝑎𝑡𝑡 + 𝑓𝑖𝑗
𝑝ℎ
+ Σ𝑏 𝑓𝑖𝑏𝑠𝑜𝑐 + 𝑓𝑖𝑏
+ Σ𝑐 𝑓𝑖𝑐𝑎𝑡𝑡
 soc: Repulsive social force
 att: Attractive social force
 ph: Physical force
Sungjoon Choi
Papers in CDC
7
INVERSE OPTIMAL CONTROL FOR DETERMINISTIC CONTINUOUS-TIME
NONLINEAR SYSTEMS
CPSLAB (http://cpslab.snu.ac.kr)
 Existing inverse reinforcement learning algorithms require feedforward learning.
 Max-margin inverse RL [Abeel and Ng]
 Maximum-margin planning [Ratliff]
 Bi-level inverse optimal control [Mombaur]
 Optimal control problems
𝑡𝑓
𝑚𝑖𝑛𝑖𝑚𝑖𝑧𝑒𝑥,𝑢
𝑐 𝑇 𝜙 𝑡, 𝑥 𝑡 , 𝑦 𝑡
𝑑𝑡
𝑡0
𝑠𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜 𝑥 𝑡 = 𝑓 𝑡, 𝑥 𝑡 , 𝑢 𝑡
 Use Hamiltonian function
 𝐻 𝑥, 𝑢, 𝑝 = 𝑐 𝑇 𝜙 𝑡, 𝑥, 𝑢 + 𝑝𝑇 𝑓 𝑡, 𝑥, 𝑢
Sungjoon Choi
Papers in CDC
8
IMPUTING A CONVEX OBJECTIVE FUNCTION
CPSLAB (http://cpslab.snu.ac.kr)
 Parametric optimization using convex optimization
 Existing IRL approaches suffer from the curse of dimensionality.
 Apply residual function to the KKT conditions.
Sungjoon
Papers in CDC
9